段金桥

2026

Artificial intelligence as a surrogate brain: bridging neural dynamical models and data

National Science Review

2026

Detecting the most probable transition phenomenon in a nutrient-phytoplankton-zooplankton system.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

DOI

2026

Nonlocal Kramers-Moyal formulas and data-driven discovery of stochastic dynamical systems with multiplicative Lévy noise

Communications in nonlinear science & numerical simulation

DOI

2026

Entropy Production and Reversibility Criteria for Stochastic Evolution Equations

2026

The Numerical Onsager-Machlup action functional for Euler discretized SDEs driven by fractional Brownian motion

2026

Data-Driven Modeling of Stochastic Delay Differential Equations with Error Mitigation and Multi-Parameter Adaptation

Journal of Computational Physics

DOI

2025

Action functional as an early warning indicator in the space of probability measures via Schr?dinger bridge

Quantitative Biology

2025

The convergence problem of the generalized Korteweg-de Vries equation in Fourier-Lebesgue space

Journal of Differential Equations

DOI

2025

Quantifying the most probable dynamics of a particle inside a sphere.

Chaos

DOI

2025

Impact of precipitation on the resilience of tropical forests to non-Gaussian Lévy fluctuations

Applied Mathematical Modelling

DOI

2025

Data driven discovery of escape phenomena in stochastic systems.

Chaos

DOI

2025

Numerical integrations of stochastic contact Hamiltonian systems via stochastic contact Hamilton-Jacobi equation

Communications in nonlinear science & numerical simulation

DOI

2025

Noise-intensity bifurcations of transition paths by Morse index formula

2025

Homogenization and corrector results for the stochastic non-homogeneous incompressible Navier-Stokes equations with rapid oscillation

2025

An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulas

Communications in nonlinear science & numerical simulation

DOI

2025

Influence of extreme events modeled by Lévy flight on Atlantic meridional overturning circulation stability

Physica A: Statistical Mechanics and its Applications

DOI

2024

Quantifying Random Collisions between Particles Inside and Outside a Circle

Physica A: Statistical Mechanics and its Applications

DOI

2024

Strichartz estimates for orthonormal functions and probabilistic convergence of density functions of compact operators on manifolds

2024

Structure-preserving methods for Marcus stochastic Hamiltonian systems with additive Lévy noise

Journal of Mathematics and Physics

DOI

2024

A deep learning method for computing mean exit time excited by weak Gaussian noise

Nonlinear dynamics

DOI

2024

Stochastic parameter reduced-order model based on hybrid machine learning approaches

arXiv.org

DOI

2024

Fourier neural operator based fluid–structure interaction for predicting the vesicle dynamics

Physica D Nonlinear Phenomena

DOI

2023

Stochastic dynamics of human papillomavirus delineates cervical cancer progression

Journal of Mathematical Biology

DOI

2023

Stochastic Perturbations in the Fractional Nonlinear Schr\"odinger Equation: Well-posedness and Blow-up

2023

Early warning indicators via latent stochastic dynamical systems.

Chaos

DOI

2023

Detecting the most probable transition pathway based on optimal control theory

Applied Mathematical Modelling

DOI

2023

Communications on Stochastic Analysis Communications on Stochastic Analysis

2023

$C^{k}$ extension and invariant manifolds for the compactification of nonautonomous systems with autonomous limits

2023

The most probable dynamics of receptor-ligand binding on cell membrane

2023

Well-posedness and wave-breaking for the stochastic rotation-two-component Camassa–Holm system

The Annals of Applied Probability

DOI

2023

Detecting stochastic governing laws with observation on stationary distributions

Physica A: Statistical Mechanics and its Applications

DOI

2023

Symplectic numerical integration for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus

Mathematics and Computers in Simulation

DOI

2023

Deep reinforcement learning in finite-horizon to explore the most probable transition pathway

Physica D Nonlinear Phenomena

DOI

2023

Stochastic dynamics and data science

Stochastics and Dynamics

DOI

2022

D ec 2 00 0 Symbolic Representations of Iterated Maps November 14 , 2000

2022

A data-driven approach for discovering the most probable transition pathway for a stochastic carbon cycle system.

Chaos

DOI

2022

A machine learning method for computing quasi-potential of stochastic dynamical systems

Nonlinear dynamics

DOI

2022

L ÉVY I NDUCED S TOCHASTIC D IFFERENTIAL E QUATION E QUIPPED WITH N EURAL N ETWORK FOR T IME S ERIES F ORECASTING

2022

Perturbation of the spectra for asymptotically constant differential operators and applications

Physica A: Statistical Mechanics and its Applications

DOI

2022

Numerical integration of stochastic contact Hamiltonian systems via stochastic Herglotz variational principle

Physica Scripta

DOI

2022

Preface for the Second Volume of the Special Issue Dedicated to the 65th Birthday of Björn Schmalfuß

Stochastics and Dynamics

DOI

2022

An Optimal Control Method to Compute the Most Likely Transition Path for Stochastic Dynamical Systems with Jumps

Chaos

DOI

2022

An end-to-end deep learning approach for extracting stochastic dynamical systems with α-stable Lévy noise

Chaos

DOI

2022

Learning effective dynamics from data-driven stochastic systems.

Chaos

DOI

2022

An Onsager-Machlup approach to the most probable transition pathway for a genetic regulatory network.

Chaos

DOI

2022

Data-driven method to learn the most probable transition pathway and stochastic differential equation

Physica A: Statistical Mechanics and its Applications

DOI

2021

Slow Manifold and Parameter Estimation for a Nonlocal Fast-Slow Dynamical System with Brownian Motion

Acta Mathematica Scientia

DOI

2021

Machine learning framework for computing the most probable paths of stochastic dynamical systems.

Physical Review E

DOI

2021

Dynamical behavior of a nonlocal Fokker-Planck equation for a stochastic system with tempered stable noise.

Chaos

DOI

2021

Stochastic turbulence for Burgers equation driven by cylindrical Lévy process

Stochastics and Dynamics

DOI

2021

Gibbs Measure for the Higher Order Modified Camassa-Holm Equation

DOI

2021

Homogenization of Dissipative Hamiltonian Systems Under Lévy Fluctuations

Journal of nonlinear science

DOI

2021

Large Deviations for SDE driven by Heavy-tailed L\'evy Processes

2021

Energetic Variation with the Anderson Hamiltonian

2021

Most Probable Transitions from Metastable to Oscillatory Regimes in a Carbon Cycle System

Chaos

DOI

2021

Neural network stochastic differential equation models with applications to financial data forecasting

Applied Mathematical Modelling

DOI

2021

Variational inference of the drift function for stochastic differential equations driven by Lévy processes.

Chaos

DOI

2021

Learning the temporal evolution of multivariate densities via normalizing flows

Chaos

DOI

2021

Discovering governing equation from data for multi-stable energy harvester under white noise

Nonlinear dynamics

DOI

2021

Detection of bistable structures via the Conley index and applications to biological systems

2021

Global well-posedness of the stochastic Camassa–Holm equation

Communications in Mathematical Sciences

DOI

2021

Time Series Forecasting with Ensembled Stochastic Differential Equations Driven by Lévy Noise

arXiv.org

2021

The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation

Nonlinearity

DOI

2021

Wave-breaking and moderate deviations of the stochastic Camassa–Holm equation with pure jump noise

DOI

2021

Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systems

Journal of statistical physics

DOI

2021

Linear Response Theory for Nonlinear Stochastic Differential Equations with $$\alpha $$-Stable Lévy Noises

DOI

2021

Extracting stochastic governing laws by non-local Kramers–Moyal formulae

Philosophical Transactions of the Royal Society A

DOI

2021

Kantorovich-Rubinstein distance and approximation for non-local Fokker-Planck equations.

Chaos

DOI

2021

Stochastic bifurcation for two-time-scale dynamical system with α-stable Lévy noise

Journal of Statistical Mechanics: Theory and Experiment

DOI

2021

The Most Likely Transition Path for a Class of Distribution-Dependent Stochastic Systems

Stochastics and Dynamics

DOI

2021

Convergence rate for homogenization of a nonlocal model with oscillating coefficients

2021

Bohmian trajectories of the time-oscillating Schrödinger equations.

Chaos

DOI

2021

Nonparametric inference of stochastic differential equations based on the relative entropy rate

Mathematical methods in the applied sciences

DOI

2021

Extracting stochastic dynamical systems with α-stable Lévy noise from data

arXiv.org

DOI

2020

Analysis of multiscale methods for stochastic dynamical systems driven by α-stable processes

Applied Mathematics Letters

DOI

2020

Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces

DOI

2020

The role of slow manifolds in parameter estimation for a multiscale stochastic system with α-stable Lévy noise

Journal of Mathematics and Physics

DOI

2020

A logistic-harvest model with allee effect under multiplicative noise

DOI

2020

Lyapunov exponents for Hamiltonian systems under small Lévy-type perturbations.

Chaos

DOI

2020

Most probable dynamics of stochastic dynamical systems with exponentially light jump fluctuations.

Chaos

DOI

2020

Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

New Journal of Physics

DOI

2020

The tipping times in an Arctic sea ice system under influence of extreme events.

Chaos

DOI

2020

Extracting Non-Gaussian Governing Laws from Data on Mean Exit Time

Chaos

DOI

2020

Diffusion approximation for diffusive time scale jump processes

2020

Numerical analysis and applications of Fokker-Planck equations for stochastic dynamical systems with multiplicative α-stable noises

DOI

2020

Dynamical Analysis of Stochastic COVID-19 Model with Jump-Diffusion

2020

Identifying stochastic governing equations from data of the most probable transition trajectories

arXiv.org

2020

State transitions in the Morris-Lecar model under stable Lévy noise

European Physical Journal B : Condensed Matter Physics

DOI

2020

Double canard cycles in singularly perturbed planar systems

Nonlinear dynamics

DOI

2020

Weak averaging principle for multiscale stochastic dynamical systems driven by stable processes

Journal of Differential Equations

DOI

2020

Probabilistic pointwise convergence problem of some dispersive equations

2020

Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance

Communications in nonlinear science & numerical simulation

DOI

2020

Estimating the most probable transition time for stochastic dynamical systems

Nonlinearity

DOI

2020

Pointwise convergence problem of Ostrovsky equation with rough data and random data

2020

Lyapunov Exponents for Stochastic Hamiltonian Systems with L\'evy noise

2020

Mean escape time for randomly switching narrow gates in a steady flow

Computers and Mathematics with Applications

DOI

2020

Effective wave factorization for a stochastic Schrödinger equation

DOI

2020

The Cauchy problem for the generalized KdV equation with rough data and random data

2020

An averaging principle for fractional stochastic differential equations with Lévy noise.

Chaos

DOI

2020

Dynamics of the Tyson–Hong–Thron–Novak circadian oscillator model

DOI

2020

Symplectic Euler scheme for Hamiltonian stochastic differential equations driven by Levy noise

arXiv.org

2020

Gevrey semigroup generated by −(Λ  + b ⋅ ∇) in Lp(Rn)

DOI

2020

Discovering transition phenomena from data of stochastic dynamical systems with Lévy noise.

Chaos

DOI

2020

Stochastic bifurcation in single-species model induced by α-stable Lévy noise

Journal of Statistical Mechanics: Theory and Experiment

DOI

2020

Stochastic regularization for transport equations

DOI

2020

A Data-Driven Approach for Discovering Stochastic Dynamical Systems with Non-Gaussian Levy Noise

arXiv.org

DOI

2020

On the abrupt change of the maximum likelihood state in a simplified stochastic thermohaline circulation system.

Chaos

DOI

2020

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks

SIAM Journal on Scientific Computing

DOI

2020

Maximum likelihood estimation of stochastic differential equations with random effects driven by fractional Brownian motion

Applied Mathematics and Computation

DOI

2020

Instability of small-amplitude periodic waves from fold-Hopf bifurcation

Journal of Mathematics and Physics

DOI

2020

Effective Approximation for a Stochastic System with Large Potential

2020

Detecting the maximum likelihood transition path from data of stochastic dynamical systems.

Chaos

DOI

2020

Influence of extreme events modeled by Lévy flight on global thermohaline circulation stability

DOI

2019

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

European journal of applied mathematics

DOI

2019

White noise driven Ostrovsky equation

Journal of Differential Equations

DOI

2019

Transitions between Ice-free and Ice-covered States in a Reduced Model

2019

Large deviations for stochastic differential equations driven by semimartingales

Teoriya Veroyatnostei i ee Primeneniya

DOI

2019

The persistence of synchronization under $\alpha$-stable noise

2019

Discovering mean residence time and escape probability from data of stochastic dynamical systems.

Chaos

DOI

2019

Effective approximation for a nonlocal stochastic Schrödinger equation with oscillating potential

Zeitschrift für Angewandte Mathematik und Physik

DOI

2019

Nonlocal Dynamics for Non-Gaussian Systems Arising in Biophysical Modeling

Communication on Applied Mathematics and Computation

DOI

2019

Effects of Lévy noise on the FitzHugh-Nagumo model: A perspective on the maximal likely trajectories.

Journal of Theoretical Biology

DOI

2019

Stochastic nonlocal conservation laws on whole space

Computers and Mathematics with Applications

DOI

2019

The influences of correlated spatially random perturbations on first passage time in a linear-cubic potential.

Chaos

DOI

2019

On Relative Category and Morse Decompositions for Dynamical Systems

2019

Maximal likely phase lines for a reduced ice growth model

Physica A: Statistical Mechanics and its Applications

DOI

2019

Effective reduction of a three-dimensional circadian oscillator model

Discrete & Continuous Dynamical Systems - B

DOI

2019

Most probable transition pathways and maximal likely trajectories in a genetic regulatory system

Physica A: Statistical Mechanics and its Applications

DOI

2019

Transitions between metastable states in a simplified model for the thermohaline circulation under random fluctuations

Applied Mathematics and Computation

DOI

2019

Large deviations for stochastic systems of slow-fast diffusions with non-Gaussian L\'evy noises.

2019

A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equations

Applied Mathematics and Computation

DOI

2019

Global solution and blow-up of the stochastic nonlinear Schrödinger system

Journal of Mathematics and Physics

DOI

2019

Slow manifolds for dynamical systems with non-Gaussian stable Lévy noise

Analysis and Applications

DOI

2019

Slow manifolds for a nonlocal fast-slow stochastic system with stable Lévy noise

Journal of Mathematics and Physics

DOI

2019

The maximum likelihood climate change for global warming under the influence of greenhouse effect and Lévy noise.

Chaos

DOI

2019

Forward attraction of pullback attractors and synchronizing behavior of gradient-like systems with nonautonomous perturbations

Discrete & Continuous Dynamical Systems - B

DOI

2019

Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation

Applied Mathematics and Computation

DOI

2019

Rolling with Random Slipping and Twisting: A Large Deviation Point of View

Stochastics and Dynamics

DOI

2019

Action Functionals for Stochastic Differential Equations with Lévy Noise

Communications on Stochastic Analysis

DOI

2018

Global Well-posedness of the Stochastic Generalized Kuramoto-Sivashinsky Equation with Multiplicative Noise

Acta Mathematicae Applicatae Sinica (English Series)

DOI

2018

Bounded and unbounded solutions of a discontinuous oscillator at resonance

International Journal of Non-Linear Mechanics

DOI

2018

Effective Reduction for a Nonlocal Zakai Stochastic Partial Differential Equation in Data Assimilation

Journal of Dynamics and Differential Equations

DOI

2018

A generalization of the Mittag–Leffler function and solution of system of fractional differential equations

Advances in Differential Equations

DOI

2018

A two-level linearized compact ADI scheme for two-dimensional nonlinear reaction-diffusion equations

Computers and Mathematics with Applications

DOI

2018

Homogenization For Some Nonlocal Stochastic Partial Differential Equation

2018

Bifurcation in Mean Phase Portraits for Stochastic Dynamical Systems with Multiplicative Gaussian Noise

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

DOI

2018

The Fokker-Planck equation in the case of multiplicative $\alpha$-stable L\'evy motion and application

2018

Most Probable Evolution Trajectories in a Genetic Regulatory System Excited by Stable L\'evy Noise

2018

Stability and convergence of compact finite difference method for parabolic problems with delay

Applied Mathematics and Computation

DOI

2018

Most probable dynamics of a genetic regulatory network under stable Lévy noise

Applied Mathematics and Computation

DOI

2018

Slow manifold and parameter estimation for a nonlocal fast-slow stochastic evolutionary system

2018

Compactly Generated Shape Index for Infinite-dimensional Local Dynamical Systems on Complete Metric Spaces

2018

Homogenization of Stable-like Feller Processes

2018

Geometric Methods for Stochastic Dynamical Systems

Stochastic PDEs and Modelling of Multiscale Complex System

DOI

2018

Fokker-Planck equation driven by asymmetric Lévy motion

Advances in Computational Mathematics

DOI

2018

Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise

DOI

2018

Boundary Blow-up Solutions to Nonlocal Elliptic Systems of Cooperative Type

DOI

2018

A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

DOI

2018

Effective Filtering Analysis for Non-Gaussian Dynamic Systems

Applied Mathematics and Optimization

DOI

2018

Effective characterization for stochastic differential equations with tempered stable L\'evy fluctuations

2018

Compactly Generated Shape Index Theory and its Application to a Retarded Nonautonomous Parabolic Equation

2018

IMPACTS OF NOISE ON ORDINARY DIFFERENTIAL EQUATIONS

DOI

2018

Lévy noise induced escape in the Morris–Lecar model

Physica A: Statistical Mechanics and its Applications

DOI

2018

Homogenization of non-symmetric jump processes

Advances in Applied Probability

DOI

2018

A Theory of Compact Hausdorff Shape in Hausdorff Spaces

2018

Long-time behavior of a class of nonlocal partial differential equations

DOI

2018

The Onsager–Machlup function as Lagrangian for the most probable path of a jump-diffusion process

Nonlinearity

DOI

2018

Fokker-Planck equations for nonlinear dynamical systems driven by multiplicative $\alpha$-stable L\'evy motions

2018

Hamiltonian systems with Lévy noise: Symplecticity, Hamilton’s principle and averaging principle

Physica A: Statistical Mechanics and its Applications

DOI

2018

A parameter estimator based on Smoluchowski-Kramers approximation

Applied Mathematics Letters

DOI

2018

A role of random slow manifolds in detecting stochastic bifurcation

2018

Linearized compact ADI schemes for nonlinear time-fractional Schrödinger equations

Applied Mathematics Letters

DOI

2018

Lévy noise induced transition and enhanced stability in a gene regulatory network.

Chaos

DOI

2018

Mean exit time for stochastic dynamical systems driven by tempered stable Lévy fluctuations

Applied Mathematics Letters

DOI

2018

Homogenization of Periodic Linear Nonlocal Partial Differential Equations

2018

Target search of a protein on DNA in the presence of position-dependent bias

Journal of Statistical Mechanics: Theory and Experiment

DOI

2018

A Newton linearized compact finite difference scheme for one class of Sobolev equations

DOI

2018

Characterization of the most probable transition paths of stochastic dynamical systems with stable Lévy noise

Journal of Statistical Mechanics: Theory and Experiment

DOI

2017

L\'{e}vy noise-induced transitions in gene regulatory networks

2017

Metastability for discontinuous dynamical systems under Lévy noise: Case study on Amazonian Vegetation

Scientific Reports

DOI

2017

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise.

Chaos

DOI

2017

Behavioral synchronization induced by epidemic spread in complex networks.

Chaos

DOI

2017

Existence and regularity of a linear nonlocal Fokker–Planck equation with growing drift

DOI

2017

Kinetic Solutions for Nonlocal Scalar Conservation Laws

SIAM Journal on Mathematical Analysis

DOI

2017

Lévy noise-induced escape in an excitable system

DOI

2017

A Wong-Zakai approximation for random invariant manifolds

DOI

2017

Data assimilation and parameter estimation for a multiscale stochastic system with α-stable Lévy noise

Journal of Statistical Mechanics: Theory and Experiment

DOI

2017

Transition events in a genetic regulatory system excited by multiplicative and asymmetric stable L\'evy noise

2017

Strong solution for stochastic transport equations with irregular drift: existence and non-existence

2017

Effective filtering on a random slow manifold

Nonlinearity

DOI

2017

The Cauchy problem for a two-dimensional generalized Kadomtsev–Petviashvili-I equation in anisotropic Sobolev spaces

Analysis and Applications

DOI

2017

Random data Cauchy problem for the wave equation on compact manifold

2017

Schauder estimates for stochastic transport-diffusion equations with Lévy processes

Journal of Mathematical Analysis and Applications

DOI

2017

Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion

Applied Mathematics and Computation

DOI

2017

Existence and uniqueness of $W^{1,r}_{loc}$-solutions for stochastic transport equations

2017

Random data Cauchy problem for a generalized KdV equation in the supercritical case

2017

Slow manifold for a nonlocal stochastic evolutionary system with fast and slow components

DOI

2016

随机偏微分方程——建模,分析与有效动力学

《数学建模及其应用》

2016

Stochastic basins of attraction for metastable states.

Chaos

DOI

2016

Transitions in a genetic transcriptional regulatory system under Lévy motion

Scientific Reports

DOI

2016

Enhancing dynamical robustness in aging networks of coupled nonlinear oscillators

DOI

2016

Competition promotes the persistence of populations in ecosystems

Scientific Reports

DOI

2016

Approximation for random stable manifolds under multiplicative correlated noises

DOI

2016

Maximum principles for nonlocal parabolic Waldenfels operators

Bulletin of Mathematical Sciences

DOI

2016

Approximation representation of parameterizing manifold and non-Markovian reduced systems for a stochastic Swift-Hohenberg equation

Applied Mathematics Letters

DOI

2016

Approximation of random invariant manifolds for a stochastic Swift-Hohenberg equation

DOI

2016

Stochastic modeling of nonlinear oscillators under combined Gaussian and Poisson white noise: a viewpoint based on the energy conservation law

DOI

2016

On a stochastic nonlocal conservation law in a bounded domain

DOI

2016

Random Data Cauchy Problem for Some Dispersive Equations

DOI

2016

Most probable dynamics of some nonlinear systems under noisy fluctuations

Communications in nonlinear science & numerical simulation

DOI

2016

Smooth solution of a nonlocal Fokker-Planck equation associated with stochastic systems with Lévy noise

Applied Mathematics Letters

DOI

2016

Quantifying model uncertainty in dynamical systems driven by non-Gaussian Lévy stable noise with observations on mean exit time or escape probability

Communications in nonlinear science & numerical simulation

DOI

2015

随机动力系统导论

《数学建模及其应用》

2015

什么是随机动力系统

《数学建模及其应用》

2015

Restoration of rhythmicity in diffusively coupled dynamical networks

Nature Communications

DOI

2015

Pull-in instability analyses for NEMS actuators with quartic shape approximation

Applied Mathematics and Mechanics

DOI

2015

Dynamical inference for transitions in stochastic systems with α-stable Lévy noise

DOI

2015

Nonlinear filtering of stochastic dynamical systems with Lévy noises

Advances in Applied Probability

DOI

2015

Centre manifolds for stochastic evolution equations

DOI

2015

Nonlocal elliptic equations involving measures

DOI

2015

Numerical methods for the mean exit time and escape probability of two-dimensional stochastic dynamical systems with non-Gaussian noises

Applied Mathematics and Computation

DOI

2015

Approximation of Random Slow Manifolds and Settling of Inertial Particles Under Uncertainty

Journal of Dynamics and Differential Equations

DOI

2015

The Cauchy problem for the Ostrovsky equation with positive dispersion

Nonlinear Differential Equations and Applications NoDEA

DOI

2015

Lyapunov exponents of stochastic differential equations driven by Lévy processes

Dynamical systems

DOI

2015

A regularity result for the nonlocal Fokker-Planck equation with Ornstein-Uhlenbeck drift

2015

A nonlocal Fokker-Planck equation for non-Gaussian stochastic dynamical systems

Applied Mathematics Letters

DOI

2015

On the shape Conley index theory of semiflows on complete metric spaces

DOI

2014

Effective Dynamics of Stochastic Partial Differential Equations

DOI

2014

Emergence of amplitude and oscillation death in identical coupled oscillators.

Physical review. E, Statistical, nonlinear, and soft matter physics

DOI

2014

Impacts of noise on a class of partial differential equations

Journal of Differential Equations

DOI

2014

Impact of Correlated Noises on Additive Dynamical Systems

DOI

2014

Stochastic Averaging Principles

DOI

2014

Derivation of Fokker-Planck equations for stochastic dynamical systems under excitation of multiplicative non-Gaussian white noise

DOI

2014

Approximation of the inertial manifold for a nonlocal dynamical system

2014

Martingale and Weak Solutions for a Stochastic Nonlocal Burgers Equation on Bounded Intervals

DOI

2014

Deterministic Partial Differential Equations

DOI

2014

Mean Exit Time and Escape Probability for Dynamical Systems Driven by Lévy Noises

SIAM Journal on Scientific Computing

DOI

2014

Slow Manifold Reduction

DOI

2014

Stochastic Calculus in Hilbert Space

DOI

2014

Chapter 7 – Stochastic Homogenization

DOI

2014

A parameter estimation method based on random slow manifolds

Applied Mathematical Modelling

DOI

2013

Lévy noise-induced stochastic resonance in a bistable system

European Physical Journal B : Condensed Matter Physics

DOI

2013

An alternative expression for stochastic dynamical systems with parametric Poisson white noise

DOI

2013

State estimation under non-Gaussian Levy noise: A modified Kalman filtering method

arXiv.org

DOI

2013

Global solutions for a nonlocal Ginzberg-Landau equation and a nonlocal Fokker-Plank equation

2013

Convergence of global attractors of a 2D non-Newtonian system to the global attractor of the 2D Navier-Stokes system

DOI

2013

Random Dynamics of the Stochastic Boussinesq Equations Driven by Lévy Noises

DOI

2013

Centre manifolds for infinite dimensional random dynamical systems

Dynamical systems

DOI

2013

Fokker-Planck equations for stochastic dynamical systems with symmetric Lévy motions

Applied Mathematics and Computation

DOI

2013

Dispersion in flows with obstacles and uncertainty

DOI

2013

Stochastic Averaging Principle for Dynamical Systems with Fractional Brownian Motion

DOI

2013

Slow foliation of a slow-fast stochastic evolutionary system

DOI

2012

Elementary bifurcations for a simple dynamical system under non-Gaussian Levy noises

DOI

2012

Quantifying Model Uncertainties in the Space of Probability Measures

DOI

2012

Global well-posedness of a stochastic coupled Kuramoto–Sivashinsky and Ginzburg–Landau-type model for the Marangoni convection

DOI

2012

Multiplicative ergodic theorem for discontinuous random dynamical systems

2012

Impact of $\alpha$-stable Lévy noise on the Stommel model for the thermohaline circulation

DOI

2012

Upper semicontinuity of Global attractors for 2D Navier-Stokes equations

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

DOI

2012

Approximating Dynamics of a Singularly Perturbed Stochastic Wave Equation with a Random Dynamical Boundary Condition

SIAM Journal on Mathematical Analysis

DOI

2012

Asymptotic methods for stochastic dynamical systems with small non-Gaussian L\'evy noise

DOI

2012

Synchronization of an evolving complex hyper-network

DOI

2012

Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Lévy processes

DOI

2012

Ensemble Averaging for Dynamical Systems Under Fast Oscillating Random Boundary Conditions

Stochastic Analysis and Applications

DOI

2012

Non-Gaussian dynamics of a tumor growth system with immunization

DOI

2012

Lyapunov exponents of discontinuous random dynamical systems

2012

Large deviations and approximations for slow–fast stochastic reaction–diffusion equations

DOI

2012

Complex projective synchronization in coupled chaotic complex dynamical systems

DOI

2012

Stationary measures for stochastic differential equations with jumps

DOI

2012

Simulating Stochastic Inertial Manifolds by a Backward-Forward Approach

SIAM Journal on Applied Dynamical Systems

DOI

2012

Slow Manifolds for Multi-Time-Scale Stochastic Evolutionary Systems

DOI

2012

Asymmetric non-Gaussian effects in a tumor growth model with immunization

DOI

2012

An alternative expression of Di Paola and Falson's formula for stochastic dynamics

2012

Topological equivalence for discontinuous random dynamical systems and applications

DOI

2012

Modeling nonlinear random vibration: Implication of the energy conservation law ∗

2011

A delay-dependent stability criterion for nonlinear stochastic delay-integro-differential equations

DOI

2011

Global Mild Solutions and Attractors for Stochastic Viscous Cahn-Hilliard Equation

DOI

2011

Asymptotic behavior for a semilinear second order evolution equation

DOI

2011

Dynamical behavior of the activator-repressor circuit model under random fluctuations

DOI

2011

Quantifying Model Uncertainties in Complex Systems

DOI

2011

Approximation of invariant foliations for stochastic dynamical systems

DOI

2011

Averaging, homogenization and slow manifolds for stochastic partial differential equations

DOI

2011

An averaging principle for stochastic dynamical systems with Lévy noise

DOI

2011

Escape Probability for Stochastic Dynamical Systems with Jumps

DOI

2011

Stochastic bifurcations in a bistable Duffing-Van der Pol oscillator with colored noise.

Physical review. E, Statistical, nonlinear, and soft matter physics

DOI

2011

A Taylor expansion approach for solving partial differential equations with random Neumann boundary conditions

Applied Mathematics and Computation

DOI

2011

A computational analysis for mean exit time under non-Gaussian Lévy noises

Applied Mathematics and Computation

DOI

2011

AN AVERAGING PRINCIPLE FOR TWO-SCALE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

DOI

2011

Asymptotic behavior of solutions for random wave equations with nonlinear damping and white noise

DOI

2011

Mean Exit Time and Escape Probability for a Tumor Growth System under Non-Gaussian noise

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

DOI

2010

Effective dynamics of a coupled microscopic-macroscopic stochastic system

DOI

2010

Large deviations for the stochastic quasigeostrophic equation with multiplicative noise

DOI

2010

Bridging the Boussinesq and primitive equations through spatio-temporal filtering

Applied Mathematics Letters

DOI

2010

An impact of noise on invariant manifolds in nonlinear dynamical systems

DOI

2010

Random attractor for the Ladyzhenskaya model with additive noise

DOI

2010

Synchronization of systems of Marcus canonical equations driven by α-stable noises☆

DOI

2010

Geometric shape of invariant manifolds for a class of stochastic partial differential equations

Journal of Mathematics and Physics

DOI

2010

Some Recent Advances in Stochastic Dynamics in Geosciences

2010

Recent development in stochastic dynamics and stochastic analysis

DOI

2010

A Sufficient Condition for Non-Explosion for a Class of Stochastic Partial Differential Equations

DOI

2010

Modeling Colored Noise by Fractional Brownian Motion

DOI

2010

Perspectives in Mathematical Sciences

DOI

2010

Rare events in the Boussinesq system with fluctuating dynamical boundary conditions

DOI

2010

Evolution systems of measures for stochastic flows

DOI

2010

Large deviations for slow-fast stochastic partial differential equations

2009

Stochastic Quantification of Missing Mechanisms in Dynamical Systems

DOI

2009

State space decomposition for non-autonomous dynamical systems

Proceedings of the Royal Society of Edinburgh. Section A Mathematics

DOI

2009

A Stochastic Approach for Parameterizing Unresolved Scales in a System with Memory

Journal of Algorithms & Computational Technology

DOI

2009

Structure of the set of bounded solutions for a class of nonautonomous second-order differential equations

DOI

2009

Pseudorandom numbers for conformal measures

DOI

2009

A sufficient condition for bifurcation in random dynamical systems

DOI

2009

Synchronization of Dissipative Dynamical Systems Driven by Non-Gaussian Lévy Noises

DOI

2009

Exponential stability of the multi-layer quasi-geostrophic ocean model with delays

DOI

2009

Random Dynamics of the Boussinesq System with Dynamical Boundary Conditions

DOI

2009

Canonical Sample Spaces for Random Dynamical Systems

DOI

2008

On global attractors for a class of nonhyperbolic piecewise affine maps

DOI

2008

Predictability in Spatially Extended Systems with Model Uncertainty

2008

Predictability in Nonlinear Dynamical Systems with Model Uncertainty

2008

Large deviations for the Boussinesq equations under random influences

DOI

2008

General matrix-valued inhomogeneous linear stochastic differential equations and applications

DOI

2008

Random chain recurrent sets for random dynamical systems

DOI

2008

An intermediate regime for exit phenomena driven by non-Gaussian Levy noises

DOI

2008

Dynamics of transport under random fluxes on the boundary

DOI

2008

Non-autonomous wave dynamics with memory --- asymptotic regularity and uniform attractor

DOI

2008

Stochastic modeling of unresolved scales in complex systems

DOI

2008

RECURRENT MOTIONS AND GLOBAL ATTRACTORS OF NONAUTONOMOUS LORENZ SYSTEMS DAVID CHEBAN AND JINQIAO DUAN

2008

Small probability events for two-layer geophysical flows under uncertainty

2007

Effective Macroscopic Dynamics of Stochastic Partial Differential Equations in Perforated Domains

SIAM Journal on Mathematical Analysis

DOI

2007

Homogenized Dynamics of Stochastic Partial Differential Equations with Dynamical Boundary Conditions

DOI

2007

Lagrangian Transport and Chaos in the near Wake of a Cylinder in the Time-periodic Regime: a Dynamical Systems Approach

2007

Slow integral manifolds for Lagrangian fluid dynamics in unsteady geophysical flows

DOI

2007

Report on the Workshop on “ Stochastic Dynamical Systems and Climate Modelling ” April 15-20 , 2007 , Banff International Research Station , Canada

2007

Exponential stability of non-autonomous stochastic partial differential equations with finite memory

DOI

2007

Large eddy simulation of stratified mixing in two-dimensional dam-break problem in a rectangular enclosed domain

DOI

2007

Global attractors and invariant measures for non-invertible planar piecewise isometric maps

DOI

2007

Reductions and Deviations for Stochastic Partial Differential Equations Under Fast Dynamical Boundary Conditions

DOI

2006

An Impact of Stochastic Dynamic Boundary Conditions on the Evolution of the Cahn-Hilliard System

DOI

2006

Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity

DOI

2006

Invariant manifold reduction for stochastic dynamical systems

2006

Uniform Attractors for Nonautonomous Wave Equations with Nonlinear Damping

SIAM Journal on Applied Dynamical Systems

DOI

2006

Invariant manifold reduction and bifurcation for stochastic partial differential equations

2006

Predictability of the Burgers dynamics under model uncertainty

DOI

2006

A DYNAMICAL APPROXIMATION FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

DOI

2006

Stochastic parameterization for large eddy simulation of geophysical flows

DOI

2005

Averaging principle for quasi-geostrophic motion under rapidly oscillating forcing

DOI

2005

具有快速振荡外力的拟地转运动的平均原理

《应用数学和力学》

2005

Feedback Stabilization for Oseen Fluid Equations: A Stochastic Approach

Journal of Mathematical Fluid Mechanics

DOI

2005

Probability and partial differential equations in modern applied mathematics

DOI

2005

Non-autonomous and stochastic dynamics of oceanic gravity currents

2004

Dynamics of the thermohaline circulation under uncertainty

Journal of Mathematical Analysis and Applications

DOI

2004

Dynamics of a coupled atmosphere–ocean model

Nonlinear Analysis: Real world applications

DOI

2004

Enstrophy and Ergodicity Of Gravity Currents

DOI

2004

Smooth Stable and Unstable Manifolds for Stochastic Evolutionary Equations

DOI

2004

A MARKOV JUMP PROCESS APPROXIMATION OF THE STOCHASTIC BURGERS EQUATION

DOI

2004

Entrainment in bottom gravity currents over complex topography from three‐dimensional nonhydrostatic simulations

DOI

2004

Exponential stability of the quasigeostrophic equation under random perturbations

DOI

2004

Almost Periodic Solutions and Global Attractors of Non-autonomous Navier–Stokes Equations

DOI

2004

Ergodic dynamics of the stochastic Swift–Hohenberg system

Nonlinear Analysis: Real world applications

DOI

2004

A Wiener–Hopf approximation technique for a multiple plate diffraction problem

DOI

2004

Ergodic dynamics of the coupled quasigeostrophic-flow-energy-balance system

DOI

2004

Recurrent motions and global attractors of non-autonomous Lorenz systems

DOI

2003

Determining functionals for random partial differential equations

DOI

2003

Dynamics of quasi-geostrophic fluid motion with rapidly oscillating Coriolis force

DOI

2003

HETEROCLINIC POINTS OF MULTI-DIMENSIONAL DYNAMICAL SYSTEMS

2003

Recurrent motions in the nonautonomous Navier-Stokes system

DOI

2003

Generalization of the second Bogolyubov's theorem for non-almost periodic systems

DOI

2003

INVARIANT MANIFOLDS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

DOI

2002

Time-periodically forced amplitude evolution in spatially extended nonlinear systems

Applied Mathematics and Computation

DOI

2002

Stochastic dynamics of a coupled atmosphere-ocean model

DOI

2001

On the stochastic Kuramoto—Sivanshinsky equation

DOI

2001

Navier-Stokes, Fluid Dynamics, and Image and Video Inpainting

2001

The effect of changing the Coriolis force gradient parameter on the escape probability and mean residence time

Applied Mathematics and Computation

DOI

2001

Dynamics of the Thermohaline Circulation under Wind Forcing

DOI

2001

Ergodicity of stochastically forced large scale geophysical flows

International Journal of Mathematics and Mathematical Sciences

DOI

2001

Probabilistic Dynamics of Two-Layer Geophysical Flows

DOI

2001

Fractional Differential Equations and Multifractality

2001

Enstrophy dynamics of stochastically forced large-scale geophysical flows

DOI

2000

Symbolic Representations of Iterated Maps

DOI

2000

Asymptotics for the Generalized Two-Dimensional Ginzburg–Landau Equation

DOI

2000

The 3D Quasigeostrophic Fluid Dynamics Under Random Forcing On Boundary

DOI

2000

On nonlinear amplitude evolution under stochastic forcing

Applied Mathematics and Computation

DOI

2000

Probabilistic structural dynamics of protein folding

Applied Mathematics and Computation

DOI

2000

The 3D quasigeostrophic equation under random perturbation

1999

关于一个扰动非线性薛定谔方程的注记(英文)

《数学杂志》

1999

Variational methods and nonlinear quasigeostrophic waves

DOI

1999

Modeling Nonlinear Phenomena by Dynamical Systems

DOI

1999

Almost periodic passive tracer dispersion

DOI

1999

APPLIED NONLINEAR STOCHASTIC DYNAMICS

DOI

1999

Escape Probability and Mean Residence Time in Random Flows with Unsteady Drift

DOI

1999

Nonlocal dynamics of passive tracer dispersion with random stopping

1999

Self-Consistent Multiscale Theory of Internal Wave, Mean-Flow Interactions

DOI

1999

Dissipative Quasi-Geostrophic Motion under Temporally Almost Periodic Forcing☆☆☆

DOI

1999

Fractional Fokker-Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises

DOI

1999

Chaoti Properties of SubshiftsGenerated by a Non-Periodi Re urrent Orbit July 1999

1999

Generalized Stable Multivariate Distribution and Anisotropic Dilations

1999

Chaotic Properties of Subshifts Generated by a Nonperiodic Recurrent Orbit

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

DOI

1999

Escape probability, mean residence time and geophysical fluid particle dynamics

DOI

1998

Dissipative Quasi-geostrophic Dynamics under Random Forcing

Journal of Mathematical Analysis and Applications

DOI

1998

Infinite-Dimensional Linear Dynamical Systems with Chaoticity

DOI

1998

Passive tracer dispersion with random or periodic source

DOI

1998

Asymptotic dynamical difference between the nonlocal and local Swift–Hohenberg models

DOI

1998

Time-periodic quasigeostrophic motion under dissipation and forcing

Applied Mathematics and Computation

DOI

1998

Dynamics of a Nonlocal Kuramoto–Sivashinsky Equation

DOI

1998

A remark on the three dimensional baroclinic quasi-geostrophic dynamics

Applied Mathematics and Computation

DOI

1998

A linear chaotic quantum harmonic oscillator

Applied Mathematics Letters

DOI

1997

On the Initial-Value Problem for the Generalized Two-Dimensional Ginzburg–Landau Equation☆

DOI

1997

Lagrangian transport and chaos in the near wake of the flow around an obstacle: a numerical implementation of lobe dynamics

DOI

1997

On a coupled Kuramoto–Sivashinsky and Ginzburg–Landau-type model for the Marangoni convection

DOI

1996

Fluid Exchange across a Meandering Jet Quasiperiodic Variability

DOI

1996

The effect of nonlocal interactions on the dynamics of the Ginzburg-Landau equation

DOI

1996

Limit set of trajectories of the coupled viscous Burgers' equations

Applied Mathematics Letters

DOI

1996

Nonlinear stability of one-layer geostrophic fronts

DOI

1995

Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation

Proceedings of the Edinburgh Mathematical Society

DOI

1994

On the Cauchy problem of a generalized Ginzburg-Landau equation

DOI

1993

Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation

DOI

1992

Global existence theory for a generalized Ginzburg-Landau equation

DOI

1988

工程中的一个非线性微分方程问题

《江汉大学学报(自然科学版)》

1985

带小参数的最优二次控制问题的一个注记

《九江学院学报(社会科学版)》

Stochastic Partial Differential Equations

DOI

2015

Stochastic Dynamics:Advances and Perspectives

Abstract of The 4th International Conference on Random Dynamical Systems & The 1st International Conference on Stochastic Dynamics

2023

Well-Posedness and Averaging Principle for Lévy-Type Mckean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions

SSRN Electronic Journal

DOI

2020

Onsager-Machlup action functional for stochastic partial differential equations with Levy noise

arXiv (Cornell University)

DOI