182 citations · 1.5k across the 227 of their papers we have counts for
32 papers · 1 filter
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…
Onsager-Machlup action functional for stochastic partial differential equations with Levy noise
Jianyu Hu, Jinqiao Duan
This work is devoted to deriving the Onsager-Machlup action functional for stochastic partial differential equations with (non-Gaussian) Levy process as well as Gaussian Brownian m…
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…
Effective Approximation for a Stochastic System with Large Potential
Ao Zhang, Jinqiao Duan
This letter is about effective approximation for a stochastic parabolic equation with a large potential in a periodic medium. Under a condition on the spectral properties of the as…
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…
The Cauchy problem for the generalized KdV equation with rough data and random data
Wei Yan, Xiangqian Yan, Jinqiao Duan +1
In this paper, we consider the Cauchy problem for the generalized KdV equation with rough data and random data. Firstly, we prove that as $t\longrigh…
Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces
Wei Yan, Yimin Zhang, Yongsheng Li +1
We consider the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili (RMKP) equation \begin{align*} \partial_{x}\left(u_{t}-β\partial_{x}^{3}u +\partial_{x}(u^{2})\right…
Symplectic method for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus
Qingyi Zhan, Jinqiao Duan, Xiaofan Li +1
A class of Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus, and the construction and numerical implementation methods of symplec…
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…
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks
Xiaoli Chen, Liu Yang, Jinqiao Duan +1
The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficient…
Linear Response Theory for Nonlinear Stochastic Differential Equations with -stable Lévy Noises
Qi Zhang, Jinqiao Duan
We consider a nonlinear stochastic differential equation driven by an -stable Lévy process (). We first obtain some regularity results for the probability density of its…
A Logistic-Harvest Model with Allee Effect under Multiplicative Noise
Almaz Tesfay, Daniel Tesfay, James Brannan +1
This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental…
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…
Symplectic Euler scheme for Hamiltonian stochastic differential equations driven by Levy noise
Qingyi Zhan, Jinqiao Duan, Xiaofan Li
This paper proposes a general symplectic Euler scheme for a class of Hamiltonian stochastic differential equations driven by Lvy noise in the sense of Marcus form. The c…
Extracting Non-Gaussian Governing Laws from Data on Mean Exit Time
Yanxia Zhang, Jinqiao Duan, Yanfei Jin +1
Motivated by the existing difficulties in establishing mathematical models and in observing the system state time series for some complex systems, especially for those driven by no…
Estimating the Most Probable Transition Time for Stochastic Dynamical Systems
Yuanfei Huang, Ying Chao, Wei Wei +1
This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic…
Pointwise convergence problem of Ostrovsky equation with rough data and random data
Wei Yan, Qiaoqiao Zhang, Jinqiao Duan +1
In this paper, we consider the pointwise convergence problem of free Ostrovsky equation with rough data and random data. Firstly, we show the almost everywhere pointwise convergenc…
Analysis of multiscale methods for stochastic dynamical systems driven by -stable processes
Yanjie Zhang, Xiao Wang, Zibo Wang +1
In this paper, we first analyze the strong and weak convergence of projective integration methods for multiscale stochastic dynamical systems driven by -stable processes, which…
Effective Wave Factorization for a Stochastic Schrödinger Equation
Ao Zhang, Jinqiao Duan
We study the homogenization of a stochastic Schrödinger equation with a large periodic potential in solid state physics. Denoting by the period, the potential is scal…
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…
A Data-Driven Approach for Discovering Stochastic Dynamical Systems with Non-Gaussian Levy Noise
Yang Li, Jinqiao Duan
With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying th…
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…