scholarly journals Exponential attractor and its fractal dimension for a second order lattice dynamical system

2010 ◽  
Vol 367 (2) ◽  
pp. 350-359 ◽  
Author(s):  
Xiaoming Fan ◽  
Han Yang
Keyword(s):  
Dynamical System ◽  
Fractal Dimension ◽  
Second Order ◽  
Exponential Attractor ◽  
Lattice Dynamical System

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 and Uniform Exponential Attractors for Nonautonomous Boussinesq Lattice System

2015 ◽  
Vol 25 (08) ◽  
pp. 1550100 ◽  
Author(s):  
Min Zhao ◽  
Shengfan Zhou
Keyword(s):  
Dynamical System ◽  
Boussinesq Equations ◽  
Lattice System ◽  
Time Dependent ◽  
Pullback Attractor ◽  
Exponential Attractor ◽  
Uniform Attractor ◽  
Exponential Attractors ◽  
Lattice Dynamical System ◽  
External Forces

We first prove the existence of a pullback attractor and a pullback exponential attractor for a nonautonomous lattice dynamical system of nonlinear Boussinesq equations affected by time-dependent coupled coefficients and forces. Then, we prove the existence of a uniform attractor and a uniform exponential attractor for the system driven by quasi-periodic external forces.

Asymptotic Dynamics of Second Order Nonautonomous Systems on Infinite Lattices

2016 ◽  
Vol 26 (01) ◽  
pp. 1650003
Author(s):  
Ahmed Y. Abdallah
Keyword(s):  
Sufficient Conditions ◽  
Second Order ◽  
Exponential Attractor ◽  
Nonlinear Part ◽  
Nonautonomous Systems ◽  
Lattice Dynamical System ◽  
Lattice Dynamical Systems ◽  
Asymptotic Dynamics ◽  
Infinite Lattices ◽  
Infinite Sequences

We have introduced abstract sufficient conditions for the existence of a uniform exponential attractor for a special family of second order nonautonomous lattice dynamical systems with quasiperiodic symbols in a standard space of infinite sequences. Compared with the lattice dynamical system in [Zhou & Zhao, 2014], here a generalized nonlinear part and weaker assumptions have been presented, kindly see Remark Remark 2.1 for more details.

scholarly journals Exponential Attractor for Lattice System of Nonlinear Boussinesq Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Min Zhao ◽  
Shengfan Zhou
Keyword(s):  
Dynamical System ◽  
Continuous Semigroup ◽  
Boussinesq Equation ◽  
Lipschitz Continuity ◽  
Lattice System ◽  
Exponential Attractor ◽  
Lattice Dynamical System ◽  
The Difference

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. Then, we provide an estimation of the tail of the difference between two solutions of the system. Finally, we obtain the existence of an exponential attractor of the system.

scholarly journals Pullback Exponential Attractor for Second Order Nonautonomous Lattice System

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shengfan Zhou ◽  
Hong Chen ◽  
Zhaojuan Wang
Keyword(s):  
Fractal Dimension ◽  
Product Space ◽  
Weighted Space ◽  
Continuous Process ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lattice System ◽  
Time Dependent ◽  
Exponential Attractor ◽  
Infinite Sequences

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. Then we prove the existence and continuity of a pullback exponential attractor for second order lattice system with time-dependent coupled coefficients in the weighted space of infinite sequences. Moreover, we obtain the upper bound of fractal dimension and attracting rate for the attractor.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

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