182 citations · 1.5k across the 227 of their papers we have counts for
99 papers · 1 filter
extension and invariant manifolds for the compactification of nonautonomous systems with autonomous limits
Shuang Chen, Jinqiao Duan
We study the compactification of nonautonomous systems with autonomous limits and related dynamics. Although the extension of the compactification was well established, a g…
Detecting Stochastic Governing Laws with Observation on Stationary Distributions
Xiaoli Chen, Hui Wang, Jinqiao Duan
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with obser…
A Data-Driven Approach for Discovering the Most Probable Transition Pathway for a Stochastic Carbon Cycle System
Jianyu Chen, Jianyu Hu, Wei Wei +1
Many natural systems exhibit tipping points where changing environmental conditions spark a sudden shift to a new and sometimes quite different state. Global climate change is ofte…
Nonparametric inference of stochastic differential equations based on the relative entropy rate
Min Dai, Jinqiao Duan, Jianyu Hu +1
The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence of big data and machine learning methodology. Discovering gover…
Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulas
Yubin Lu, Yang Li, Jinqiao Duan
With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems fro…
Detection of bistable structures via the Conley index and applications to biological systems
Junbo Jia, Pan Yang, Huaiping Zhu +3
Bistability is a ubiquitous phenomenon in life sciences. In this paper, two kinds of bistable structures in dynamical systems are studied: One is two one-point attractors, another…
Dynamical behavior of a nonlocal Fokker-Planck equation for a stochastic system with tempered stable noise
Li Lin, Jinqiao Duan, Xiao Wang +1
We characterize a stochastic dynamical system with tempered stable noise, by examining its probability density evolution. This probability density function satisfies a nonlocal Fok…
On the abrupt change of the maximum likelihood state in a simplified stochastic thermohaline circulation system
Fang Yang, Xu Sun, Jinqiao Duan
The maximum likelihood state for a simplified stochastic thermohaline circulation model is investigated. It is shown that a jump occurs for the maximum likelihood state during tran…
Instability of small-amplitude periodic waves from fold-Hopf bifurcation
Shuang Chen, Jinqiao Duan
We study the existence and stability of small-amplitude periodic waves emerging from fold-Hopf equilibria in a system of one reaction-diffusion equation coupled with one ordinary d…
Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance
Yayun Zheng, Fang Yang, Jinqiao Duan +1
Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation…
Lyapunov Exponents for Hamiltonian Systems under Small Lévy Perturbations
Ying Chao, Pingyuan Wei, Jinqiao Duan
This work is to investigate the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian Lévy noise. In a suitable moving frame, the linearisation of suc…
Stochastic Bifurcation in Single-Species Model Induced by α-Stable Levy Noise
Almaz Tesfay, Daniel Tesfay, Shenglan Yuan +2
Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bif…
Dynamics of the Tyson-Hong-Thron-Novak circadian oscillator model
Shuang Chen, Jinqiao Duan, Ji Li
We study the dynamics of a circadian oscillator model which was proposed by Tyson, Hong, Thron and Novak. This model indicates a molecular mechanism for the circadian rhythm in Dro…
Weak averaging principle for multiscale stochastic dynamical systems driven by stable processes
Yanjie Zhang, Qiao Huang, Xiao Wang +2
We study the averaging principle for a family of multiscale stochastic dynamical systems. The fast and slow components of the systems are driven by two independent stable Lévy nois…
Double canard cycles in singularly perturbed planar systems with two canard points
Shuang Chen, Jinqiao Duan, Ji Li
We consider double canard cycles including two canards in singularly perturbed planar systems with two canard points. Previous work studied the complex oscillations including relax…
Detecting the maximum likelihood transition path from data of stochastic dynamic systems
Min Dai, Ting Gao, Yubin Lu +2
In recent years, the discovery of complex dynamic systems in various fields through data-driven methods has attracted widespread attention. This method has played the role of data…
The role of slow manifolds in parameter estimation for a multiscale stochastic system with -stable Lévy noise
Ying Chao, Pingyuan Wei, Jinqiao Duan
This work is about parameter estimation for a fast-slow stochastic system with non-Gaussian -stable Lévy noise. When the observations are only available for slow components, a s…
Maximal Likely Phase Lines for a Reduced Ice Growth Model
Athanasios Tsiairis, Pingyuan Wei, Ying Chao +1
We study the impact of Brownian noise on transitions between metastable equilibrium states in a stochastic ice sheet model. Two methods to accomplish different objectives are emplo…
Effective reduction of a three-dimensional circadian oscillator model
Shuang Chen, Jinqiao Duan, Ji Li
We investigate the dynamics of a three-dimensional system modeling a molecular mechanism for the circadian rhythm in Drosophila. We first prove the existence of a compact attractor…
On Relative Category and Morse Decompositions for Infinite-Dimensional Dynamical Systems
Jintao Wang, Desheng Li
We employ the relative category to develop relations between the Ważewski pair and the Morse decomposition of the maximal invariant set in $\ol{N\sm E}$ for infinite-dimens…
Discovering mean residence time and escape probability from data of stochastic dynamical systems
Dengfeng Wu, Miaomiao Fu, Jinqiao Duan
We present a method to learn mean residence time and escape probability from data modeled by stochastic differential equations. This method is a combination of machine learning fro…
Action functionals for stochastic differential equations with Lévy noise
Shenglan Yuan, Jinqiao Duan
By using large deviation theory that deals with the decay of probabilities of rare events on an exponential scale, we study the longtime behaviors and establish action functionals…
State transitions in the Morris-Lecar model under stable Lévy noise
Rui Cai, Yancai Liu, Jinqiao Duan +1
This paper considers the state transition of the stochastic Morris-Lecar neuronal model driven by symmetric -stable Lévy noise. The considered system is bistable: a stable fixed…
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…