7 citations · 7 across the 11 of their papers we have counts for
11 papers
Structural stability for the bidirectional cyclic negative feedback systems
Xu Cheng, Yi Wang, Dun Zhou
We establish the generic Kupka--Smale property for bidirectional cyclic negative feedback systems on open convex domains in the compact-open topology. Under an inward-pointin…
Dynamics of a class of time-period strongly 2-cooperative system: integer-valued Lyapunov function and embedding property of limit sets
Mengmeng Gao, Dun Zhou
We construct an integer-valued Lyapunov function for generalized negative cyclic feedback system; and prove that on any -limit set which generated by Poinc…
The Morse Smale property for time-periodic scalar reaction-diffusion equation on the circle
Tingting Su, Dun Zhou
\begin{abstract} We study the Morse-Smale property for the following scalar semilinear parabolic equation on the circle , \begin{equation*} u_{t}=u_{xx}+f(t,u,u_{x}),\,\,t>0,\…
Robust dynamics of non-autonomous systems with nested invariant cone structures
Dun Zhou
We develop a perturbation theory for skew-product semiflows with nested invariant cone (NIC) structures over compact almost periodic minimal flows. The theory describes how the res…
Non-wandering points for autonomous/periodic parabolic equations on the circle
Wenxian Shen, Yi Wang, Dun Zhou
We study the properties of non-wandering points of the following scalar reaction-diffusion equation on the circle , \begin{equation*} u_{t}=u_{xx}+f(t,u,u_{x}),\,\,t>0,\,x\in…
Almost automorphically forced flows on or in one-dimensional almost periodic semilinear heat equations
Wenxian Shen, Yi Wang, Dun Zhou
In this paper, we consider the asymptotic dynamics of the skew-product semiflow generated by the following time almost-periodically forced scalar reaction-diffusion equation \begin…
Spatial-Homogeneity of Stable Solutions of Almost-Periodic Parabolic Equations with Concave Nonlinearity
Yi Wang, Jianwei Xiao, Dun Zhou
We study the spatial-homogeneity of stable solutions of almost-periodic parabolic equations. It is shown that if the nonlinearity satisfies a concave or convex condition, then any…
Asymptotic behavior of semilinear parabolic equations on the circle with time almost-periodic/recurrent dependence
Wenxian Shen, Yi Wang, Dun Zhou
We study topological structure of the -limit sets of the skew-product semiflow generated by the following scalar reaction-diffusion equation \begin{equation*} u_{t}=u_{xx}+f(t,u…
Structure of -limit Sets for Almost-periodic Parabolic Equations on with Reflection Symmetry
Wenxian Shen, Yi Wang, Dun Zhou
The structure of the -limit sets is thoroughly investigated for the skew-product semiflow which is generated by a scalar reaction-diffusion equation \begin{equation*} u_{t}=u_{x…
Almost Automorphically and Almost Periodically Forced Circle Flows of Almost Periodic Parabolic Equations on S^1
Wenxian Shen, Yi Wang, Dun Zhou
We consider the skew-product semiflow which is generated by a scalar reaction-diffusion equation \begin{equation*} u_{t}=u_{xx}+f(t,u,u_{x}),\,\,t>0,\,x\in S^{1}=\mathbb{R}/2π\math…
Transversality for Cyclic Negative Feedback Systems
Yi Wang, Dun Zhou
Transversality of stable and unstable manifolds of hyperbolic periodic trajectories is proved for monotone cyclic systems with negative feedback. Such systems in general are not in…