scholarly journals Upper semicontinuity of the attractor for a second order lattice dynamical system

2005 ◽  
Vol 5 (4) ◽  
pp. 899-916 ◽  
Author(s):  
Ahmed Y. Abdallah ◽  
Keyword(s):  
Dynamical System ◽  
Upper Semicontinuity ◽  
Second Order ◽  
Lattice Dynamical System

scholarly journals Upper semicontinuity of the attractor for lattice dynamical systems of partly dissipative reaction diffusion systems

2005 ◽  
Vol 2005 (3) ◽  
pp. 273-288 ◽  
Author(s):  
Ahmed Y. Abdallah
Keyword(s):  
Dynamical System ◽  
Hilbert Space ◽  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Dimensional Lattice ◽  
Reaction Diffusion Systems ◽  
Infinite Dimensional ◽  
Diffusion Systems ◽  
Lattice Dynamical System ◽  
Lattice Dynamical Systems

We investigate the existence of a global attractor and its upper semicontinuity for the infinite-dimensional lattice dynamical system of a partly dissipative reaction diffusion system in the Hilbert spacel2×l2. Such a system is similar to the discretized FitzHugh-Nagumo system in neurobiology, which is an adequate justification for its study.

scholarly journals Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation

2005 ◽  
Vol 2005 (6) ◽  
pp. 655-671 ◽  
Author(s):  
Ahmed Y. Abdallah
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Global Attractor ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
Upper Semicontinuity ◽  
Time Variable ◽  
Finite Dimensional ◽  
Lattice Dynamical System ◽  
Second Order In Time

We will study the lattice dynamical system of a nonlinear Boussinesq equation. Our objective is to explore the existence of the global attractor for the solution semiflow of the introduced lattice system and to investigate its upper semicontinuity with respect to a sequence of finite-dimensional approximate systems. As far as we are aware, our result here is the first concerning the lattice dynamical system corresponding to a differential equation of second order in time variable and fourth order in spatial variable with nonlinearity involving the gradients.

ATTRACTORS FOR A LATTICE DYNAMICAL SYSTEM GENERATED BY NON-NEWTONIAN FLUIDS MODELING SUSPENSIONS

2010 ◽  
Vol 20 (09) ◽  
pp. 2681-2700 ◽  
Author(s):  
JOSÉ M. AMIGÓ ◽  
ÁNGEL GIMÉNEZ ◽  
FRANCISCO MORILLAS ◽  
JOSÉ VALERO
Keyword(s):  
Dynamical System ◽  
Upper Semicontinuity ◽  
Global Attractors ◽  
Euler Method ◽  
Equation Modeling ◽  
Suspension Flows ◽  
Upper Semicontinuous ◽  
Implicit Euler Method ◽  
Finite Dimensional ◽  
Lattice Dynamical System

In this paper we consider a lattice dynamical system generated by a parabolic equation modeling suspension flows. We prove the existence of a global compact connected attractor for this system and the upper semicontinuity of this attractor with respect to finite-dimensional approximations. Also, we obtain a sequence of approximating discrete dynamical systems by the implementation of the implicit Euler method, proving the existence and the upper semicontinuous convergence of their global attractors.

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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