182 citations · 1.5k across the 227 of their papers we have counts for
14 papers · 2 filters
Most probable dynamics of a genetic regulatory network under stable Lévy noise
Xiaoli Chen, Fengyan Wu, Jinqiao Duan +2
Numerous studies have demonstrated the important role of noise in the dynamical behaviour of a complex system. The most probable trajectories of nonlinear systems under the influen…
Characterization of the Most Probable Transition Paths of Stochastic Dynamical Systems with Stable Lévy Noise
Yuanfei Huang, Ying Chao, Shenglan Yuan +1
This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric -stable Lévy motion () or Brown…
Hamiltonian Systems with Lévy Noise: Symplecticity, Hamilton's Principle and Averaging Principle
Pingyuan Wei, Ying Chao, Jinqiao Duan
This work focuses on topics related to Hamiltonian stochastic differential equations with Lévy noise. We first show that the phase flow of the stochastic system preserves symplecti…
Bifurcation in mean phase portraits for stochastic dynamical systems with multiplicative Gaussian noise
Hui Wang, Athanasios Tsiairis, Jinqiao Duan
We investigate the bifurcation phenomena for stochastic systems with multiplicative Gaussian noise, by examining qualitative changes in mean phase portraits. Starting from the Fokk…
Geometric Methods for Stochastic Dynamical Systems
Jinqiao Duan, Hui Wang
Noisy fluctuations are ubiquitous in complex systems. They play a crucial or delicate role in the dynamical evolution of gene regulation, signal transduction, biochemical reactions…
Lévy noise induced escape in the Morris-Lecar model
Yancai Liu, Rui Cai, Jinqiao Duan
The phenomenon of an excitable system producing a pulse under external or internal stimulation may be interpreted as a stochastic escape problem. This work addresses this issue by…
Numerical analysis and applications of Fokker-Planck equations for stochastic dynamical systems with multiplicative -stable noises
Yanjie Zhang, Xiao Wang, Qiao Huang +2
The Fokker-Planck equations (FPEs) for stochastic systems driven by additive symmetric -stable noises may not adequately describe the time evolution for the probability densitie…
Mean exit time for stochastic dynamical systems driven by tempered stable Lévy fluctuations
Yanjie Zhang, Xiao Wang, Jinqiao Duan
We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered Lévy fluctuations, which are solutions of nonlocal elliptic…
Slow manifold and parameter estimation for a nonlocal fast-slow stochastic evolutionary system
Hina Zulfiqar, Ziying He, Meihua Yang +1
We establish a slow manifold for a fast-slow stochastic evolutionary system with anomalous diffusion, where both fast and slow components are influ- enced by white noise. Furthermo…
A role of random slow manifolds in detecting stochastic bifurcation
Ziying He, Rui Cai, Jinqiao Duan +1
We consider the relation for the stochastic equilibrium states between the reduced system on a random slow manifold and the original system. This provides a theoretical basis for t…
Fokker-Planck equation driven by asymmetric Lévy motion
Xiao Wang, Wenpeng Shang, Xiaofan Li +2
Non-Gaussian Lévy noises are present in many models for understanding underlining principles of physics, finance, biology and more. In this work, we consider the Fokker-Planck equa…
Compactly Generated Shape Index Theory and its Application to a Retarded Nonautonomous Parabolic Equation
Jintao Wang, Jinqiao Duan, Desheng Li
We establish the compactly generated shape (H-shape) index theory for local semiflows on complete metric spaces via more general shape index pairs, and define the H-shape cohomolog…
A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits
Hui Wang, Xiaoli Chen, Jinqiao Duan
We study stochastic bifurcation for a system under multiplicative stable Levy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium…
Data assimilation and parameter estimation for a multiscale stochastic system with alpha-stable Levy noise
Yanjie Zhang, Zhuan Cheng, Xinyong Zhang +3
This work is about low dimensional reduction for a slow-fast data assimilation system with non-Gaussian stable Lévy noise via stochastic averaging. When the observations are on…