Results 1 to 10 of about 1,344,372 (340)
The Existence of Exponential Attractor for Discrete Ginzburg-Landau Equation [PDF]
Discrete Dynamics in Nature and Society, 2015 This paper studies the following discrete systems of the complex Ginzburg-Landau equation: iu˙m-(α-iε)(2um-um+1-um-1)+iκum+βum2σum=gm, m∈Z. Under some conditions on the parameters α, ε, κ, β, and σ, we prove the existence of exponential attractor for ...
Guangyin Du, Zeqi Zhu, Caidi Zhao
doaj +6 more sources
The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System [PDF]
The Scientific World Journal, 2016 First, for a process U(t,τ)∣t≥τ, we introduce a new concept, called the weak D-pullback exponential attractor, which is a family of sets M(t)∣t≤T, for any T∈R, satisfying the following: (i) M(t) is compact, (ii) M(t) is positively invariant, that is, U(t,
Yongjun Li, Xiaona Wei, Yanhong Zhang
doaj +4 more sources
Number of attractors in the critical Kauffman model is exponential [PDF]
arXiv, 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
arxiv +8 more sources
Exponential Attractor for a First-Order Dissipative Lattice Dynamical System [PDF]
Journal of Applied Mathematics, 2008 We construct an exponential attractor for a first-order dissipative lattice dynamical system arising from spatial discretization of reaction-diffusion equations in ℝ𝑘. And we obtain fractal dimension of the exponential attractor.
Xiaoming Fan
doaj +3 more sources
The Exponential Attractors for the g-Navier-Stokes Equations [PDF]
Journal of Function Spaces and Applications, 2012 We consider the exponential attractors for the two-dimensional g-Navier-Stokes equations in bounded domain Ω. We establish the existence of the exponential attractor in L2(Ω).
Delin Wu, Jicheng Tao
doaj +5 more sources
Chevron pattern equations: exponential attractor and global stabilization [PDF]
arXiv, 2021 The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential attractor and the stabilization of the zero steady state solution through application of a finite-dimensional feedback control is proved in two spatial dimensions.
Habiba Kalantarova +2 more
arxiv +9 more sources
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
doaj +4 more sources
A necessary and sufficient condition for the existence of an exponential attractor
Open Mathematics, 2003 We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces.
Pražák Dalibor
doaj +4 more sources
Mathematical Biosciences and Engineering, 2020 In this paper we introduce a method of global exponential attractor in the reaction-diffusion epidemic model in spatial heterogeneous environment to study the spread trend and long-term dynamic behavior of the COVID-19 epidemic.
Cheng-Cheng Zhu, Jiang Zhu
doaj +2 more sources
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
openalex +11 more sources