2 citations · 6 across the 7 of their papers we have counts for
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Synchronization by degenerate noise
Xianming Liu, Xu Sun
In this paper, we derive several criteria for (weak) synchronization by noise without the global swift transitivity property. Our sufficient conditions for (weak) synchronization a…
The random dynamical pitchfork bifurcation with additive Lévy noises
Ziying He, Xianming Liu
This paper concerns the effects of additive non-Gaussian Lévy noises on the pitchfork bifurcation. We consider two types of noises, -stable process and the truncated process. Un…
A Wong-Zakai Approximation for Random Slow Manifolds with Application to Parameter Estimation
Ziying He, Xinyong Zhang, Tao Jiang +1
We study a Wong-Zakai approximation for the random slow manifold of a slow-fast stochastic dynamical system. We first deduce the existence of the random slow manifold about an appr…
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…
Small noise approximation of center manifolds for stochastic dynamical systems
Jian Ren, Zhongkai Guo, Xianming Liu +1
This paper provides a small noise approximation for local random center manifolds of a class of stochastic dynamical systems in Euclidean space. An example is presented to illustra…
Synchronization of dissipative dynamical systems driven by non-Gaussian Levy noises
Xianming Liu, Jinqiao Duan, Jicheng Liu +1
Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation and theory. However, complex systems in engineering and science are often subje…