182 citations · 1.5k across the 227 of their papers we have counts for
16 papers · 1 filter
Global Solution and Blow-up of the Stochastic Nonlinear Schrödinger system
Qi Zhang, Jinqiao Duan, Yong Chen
We study the stochastic Nonlinear Schrödinger system with multiplicative white noise in energy space . Based on deterministic and stochastic Strichartz estimates, we prove the…
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…
The persistence of synchronization under -stable noise
Yanjie Zhang, Li Lin, Jinqiao Duan +1
This work is about the synchronization of nonlinear coupled dynamical systems driven by -stable noise. Firstly, we provide a novel technique to construct the relationship betwee…
Learning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements
Xiaoli Chen, Jinqiao Duan, George Em Karniadakis
Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the so…
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…
Rolling with Random Slipping and Twisting: A Large Deviation Point of View
Qiao Huang, Wei Wei, Jinqiao Duan
We study a rolling model from the perspective of probability. More precisely, we consider a Riemannian manifold rolling against Euclidean space, where the rolling is coupled with r…
Large Deviations for Stochastic Differential Equations Driven by Semimartingales
Qiao Huang, Wei Wei, Jinqiao Duan
We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of dr…
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…
The maximum likelihood climate change for global warming under the influence of greenhouse effect and Lévy noise
Yayun Zheng, Fang Yang, Jinqiao Duan +3
An abrupt climatic transition could be triggered by a single extreme event, an -stable non-Gaussian Lévy noise is regarded as a type of noise to generate such extreme events. In…
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…
Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation
Jintao Wang, Lu Yang, Jinqiao Duan
We consider recurrent solutions of the nonautonomous modified Swift-Hohenberg equation We employ Conley index theory to show that, if…
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…
Effective Approximation for a Nonlocal Stochastic Schrödinger Equation with Oscillating Potential
Li Lin, Meihua Yang, Jinqiao Duan
We study the effective approximation for a nonlocal stochastic Schrodinger equation with a rapidly oscillating, periodically time-dependent potential. We use the natural diffusive…
Transitions between Metastable States in a Simplified Model for the Thermohaline Circulation under Random Fluctuations
Daniel Tesfay, Pingyuan Wei, Yayun Zheng +2
In this work, we study the impact of non-Gaussian alpha-stable Levy motion on transitions between metastable equilibrium states (or attractors) in a stochastic Stommel two-box mode…
Slow manifolds for a nonlocal fast-slow stochastic evolutionary system with stable Levy noise
Hina Zulfiqar, Shenglan Yuan, Ziying He +1
This work aims at understanding the slow dynamics of a nonlocal fast-slow stochastic evolutionary system with stable Levy noise. Slow manifolds along with exponential tracking prop…