182 citations · 1.5k across the 227 of their papers we have counts for
20 papers · 1 filter
Approximation of Random Slow Manifolds and Settling of Inertial Particles under Uncertainty
Jian Ren, Jinqiao Duan, Christopher K. R. T. Jones
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtai…
Synchronization of an evolving complex hyper-network
Zhaoyan Wu, Jinqiao Duan, Xinchu Fu
In this paper, the synchronization in a hyper-network of coupled dynamical systems is investigated for the first time. An evolving hyper-network model is proposed for better descri…
Asymmetric non-Gaussian effects in a tumor growth model with immunization
Mengli Hao, Jinqiao Duan, Renming Song +1
The dynamical evolution of a tumor growth model, under immune surveillance and subject to asymmetric non-Gaussian -stableLévy noise, is explored. The lifetime of a tumor staying…
Center manifolds for stochastic evolution equations
Xiaopeng Chen, A. J. Roberts, Jinqiao Duan
Stochastic invariant manifolds are crucial in modelling the dynamical behavior of dynamical systems under uncertainty. Under the assumption of exponential trichotomy, existence and…
Topological equivalence for discontinuous random dynamical systems and applications
Huijie Qiao, Jinqiao Duan
After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differ…
Stationary Measures for Stochastic Differential Equations with Jumps
Huijie Qiao, Jinqiao Duan
In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through…
Approximating dynamics of a singularly perturbed stochastic wave equation with a random dynamical boundary condition
Guanggan Chen, Jinqiao Duan, Jian Zhang
This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting skill is used to derive the approximat…
Ensemble Averaging for Dynamical Systems under Fast Oscillating Random Boundary Conditions
Wei Wang, Jian Ren, Jinqiao Duan +1
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principl…
Non-Gaussian dynamics of a tumor growth system with immunization
Mengli Hao, Ting Gao, Jinqiao Duan +1
This paper is devoted to exploring the effects of non-Gaussian fluctuations on dynamical evolution of a tumor growth model with immunization, subject to non-Gaussian α-stable type…
Lévy Noise-Induced Stochastic Resonance in a Bistable System
Yong Xu, Juanjuan Li, Jing Feng +3
Stochastic resonance phenomenon induced by non-Gaussian Lévy noise in a second-order bistable system is investigated. The signal-noise-ratio for different parameters is computed by…
Simulating Stochastic Inertial Manifolds by a Backward-Forward Approach
Xingye Kan, Jinqiao Duan, Ioannis G. Kevrekidis +1
A numerical approach for the approximation of inertial manifolds of stochastic evolutionary equations with multiplicative noise is presented and illustrated. After splitting the st…
Modeling nonlinear random vibration: Implication of the energy conservation law
Xu Sun, Jinqiao Duan, Xiaofan Li
Nonlinear random vibration under excitations of both Gaussian and Poisson white noises is considered. The model is based on stochastic differential equations, and the corresponding…
Effective dynamics of stochastic wave equation with a random dynamical boundary condition
Guanggan Chen, Jinqiao Duan, Jian Zhang
This work is devoted to the effective macroscopic dynamics of a weakly damped stochastic nonlinear wave equation with a random dynamical boundary condition. The white noises are ta…
Slow Manifolds for Multi-Time-Scale Stochastic Evolutionary Systems
Hongbo Fu, Xianming Liu, Jinqiao Duan
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of f…
Quantifying Model Uncertainties in the Space of Probability Measures
Jinqiao Duan, Ting Gao, Guowei He
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus con…
A Multiplicative Ergodic Theorem for Discontinuous Random Dynamical Systems and Applications
Huijie Qiao, Jinqiao Duan
Motivated by studying stochastic systems with non-Gaussian Lévy noise, spectral properties for a type of linear cocycles are considered. These linear cocycles have countable jump d…
An alternative expression of Di Paola and Falson's formula for stochastic dynamics
Xu Sun, Jinqiao Duan, Xiaofan Li
Di Paola and Falsone's formula is widely used in studying stochastic dynamics of nonlinear systems under Poisson white noise. In this short communication, an alternative expression…
Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Levy processes
Xu Sun, Jinqiao Duan
The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertain…
Elementary bifurcations for a simple dynamical system under non-Gaussian Levy noises
Huiqin Chen, Jinqiao Duan, Chengjian Zhang
Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a param…
Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noise
Huijie Qiao, Jinqiao Duan
The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric -stable Lévy motions. Since escape probabilities are solutions of…