scholarly journals Exponential Attractor for a First-Order Dissipative Lattice Dynamical System

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaoming Fan
Keyword(s):  
Dynamical System ◽  
Fractal Dimension ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Exponential Attractor ◽  
Spatial Discretization ◽  
First Order ◽  
Lattice Dynamical System

We construct an exponential attractor for a first-order dissipative lattice dynamical system arising from spatial discretization of reaction-diffusion equations in . And we obtain fractal dimension of the exponential attractor.

Pullback Exponential Attractors for Nonautonomous Reaction–Diffusion Equations

2015 ◽  
Vol 25 (05) ◽  
pp. 1550063
Author(s):  
Xingjie Yan ◽  
Wei Qi
Keyword(s):  
A Priori ◽  
Reaction Diffusion ◽  
A Priori Estimate ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Exponential Attractor ◽  
Exponential Attractors ◽  
Estimate Method ◽  
Necessary And Sufficient ◽  
Asymptotic A Priori Estimate

This paper presents a necessary and sufficient condition to prove the existence of the pullback exponential attractor. The asymptotic a priori estimate method is used to produce an abstract result on the existence of the pullback exponential attractor in a strong space without regularity. The established results are illustrated by applying them to the nonautonomous reaction–diffusion equations to prove the existence of the pullback exponential attractors in L2(Ω), [Formula: see text] and Lp(Ω)(p > 2) spaces.

scholarly journals Global stability and persistence in diffusive food chains

2001 ◽  
Vol 43 (2) ◽  
pp. 247-268 ◽  
Author(s):  
Yang Kuang
Keyword(s):  
Dynamical System ◽  
Steady State ◽  
Global Stability ◽  
Invariance Principle ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Food Chains ◽  
Liapunov Functional ◽  
Positive Steady State

AbstractIn this paper, the results of Freedman and So [13] on global stability and persistence of simple food chains are extended to general diffusive food chains. For global stability of the unique homogeneous positive steady state, our approach involves an application of the invariance principle of reaction-diffusion equations and the construction of a Liapunov functional. For persistence, we use the dynamical system results of Dunbar et al. [11] and Hutson and Moran [29].

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