Exponential Attractor for Lattice System of Nonlinear Boussinesq Equation
Discrete Dynamics in Nature and Society, 2013 We study the lattice dynamical system of a nonlinear Boussinesq equation. We first verify the Lipschitz continuity of the continuous semigroup associated with the system.
Min Zhao, Shengfan Zhou
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EXPONENTIAL ATTRACTOR FOR HINDMARSH-ROSE EQUATIONS IN NEURODYNAMICS [PDF]
Journal of Applied Analysis & Computation, 2019 The existence of an exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain originated in the study of neurodynamics is proved through uniform estimates together with a new theorem on the squeezing property ...
Chi Phan, Y. You
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Pullback Exponential Attractor for Second Order Nonautonomous Lattice System
Discrete Dynamics in Nature and Society, 2014 We first present some sufficient conditions for the existence of a pullback exponential attractor for continuous process on the product space of the weighted spaces of infinite sequences.
Shengfan Zhou, Hong Chen, Zhaojuan Wang
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A necessary and sufficient condition for the existence of an exponential attractor
Open Mathematics, 2003 Abstract We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction.
Pražák Dalibor
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On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis [PDF]
Discrete & Continuous Dynamical Systems - A, 2017 In this article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis.
M. Efendiev, A. Zhigun
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Exponential Attractors for Parabolic Equations with Dynamic Boundary Conditions [PDF]
Journal of Applied Mathematics, 2013 We study exponential attractors for semilinear parabolic equations with dynamic boundary conditions in bounded domains. First, we give the existence of the exponential attractor in by proving that the corresponding semigroup satisfies the enhanced ...
Zhao-hui Fan
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Pullback Exponential Attractors for Nonautonomous Klein-Gordon-Schrödinger Equations on Infinite Lattices [PDF]
Abstract and Applied Analysis, 2013 This paper proves the existence of the pullback exponential attractor for the process associated to the nonautonomous Klein-Gordon-Schrödinger equations on infinite lattices.
Chunqiu Li, Min Zhao, Caidi Zhao
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Number of Attractors in the Critical Kauffman Model Is Exponential [PDF]
Physical Review Letters, 2023 The Kauffman model is the archetypal model of genetic computation. It highlights the importance of criticality, at which many biological systems seem poised. In a series of advances, researchers have honed in on how the number of attractors in the critical regime grows with network size. But a definitive answer has proved elusive.
T. M. A. Fink, Forrest Sheldon
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Exponential attractor for Kirchhoff model with time delay and thermal effect
Results in Applied Mathematics, 2023 The Kirchhoff model is derived from the vibration problem of stretchable strings. In this paper, we focus on the long-time dynamics of the Kirchhoff model with time delay and thermal effect.
Penghui Lv, Guoguang Lin
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Exponential attractors for random dynamical systems and applications [PDF]
Stochastic Partial Differential Equations: Analysis and Computations, 2013 The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE's. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then apply these results to a nonlinear reaction-diffusion system with a random perturbation.
Armen Shirikyan, Sergey Zelik
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