Add to ORKGAbstract. We describe coupled map lattices (CML) of unbounded media corresponding to some well-known evolution partial dier-ential equations (including reaction-diusion equation, Kuramoto-Sivashinsky, Swift-Hohenberg and Ginzburg-Landau equation). Fol-lowing Kaneko we view CML also as phenomenological models of the medium and present the dynamical system approach to study the global behavior of solutions of CML. In particular, we establish spatio-temporal chaos associated with the set of traveling wave so-lutions of CML as well as describe the dynamics of the evolution operator on this set. Several examples are given to illustrate the appearance of Smale horseshoes and the presence of the dynamics of Morse-Smale type
We prove that the attractor of the 1D quintic complex Ginzburg-Landau equation with a broken phase s...
. In this paper recent work on the dynamics of lattice differential equations is surveyed. In partic...
There has been revival of interest in Jerky flow from the point of view of dynamical systems. The ea...
Abstract. In this paper, a discrete version of a reaction-diffusion equation, also known as coupled ...
AMS(MOS) Subject Classification: 34C35, 54H70, 58F10, 58F14.A class of coupled map lattices are cons...
We survey recent results in the theory of lattice differential equations. Such equations yield conti...
AbstractIn this paper, we study the existence and stability of traveling waves in lattice dynamical ...
Abstract. The reaction-diffusion equation for the Brusselator model pro-duces a coupled map lattice ...
23 pagesWe study the continuum space-time limit of a periodic one dimensional array of deterministic...
We investigate pattern formation and evolution in coupled map lattices when advection is incorporate...
This paper is mainly concerned with a kind of coupled map lattices (CMLs). New definitions of dense ...
A new method for the identification of nonlinear Coupled Map Lattice (CML) equations from measured s...
This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and in...
It is investigated how a spatial quenched disorder modifies the dynamics of coupled map lattices. Th...
The paper presents a simple mathematical model called a coupled map lattice (CML). For some range of...
We prove that the attractor of the 1D quintic complex Ginzburg-Landau equation with a broken phase s...
. In this paper recent work on the dynamics of lattice differential equations is surveyed. In partic...
There has been revival of interest in Jerky flow from the point of view of dynamical systems. The ea...
Abstract. In this paper, a discrete version of a reaction-diffusion equation, also known as coupled ...
AMS(MOS) Subject Classification: 34C35, 54H70, 58F10, 58F14.A class of coupled map lattices are cons...
We survey recent results in the theory of lattice differential equations. Such equations yield conti...
AbstractIn this paper, we study the existence and stability of traveling waves in lattice dynamical ...
Abstract. The reaction-diffusion equation for the Brusselator model pro-duces a coupled map lattice ...
23 pagesWe study the continuum space-time limit of a periodic one dimensional array of deterministic...
We investigate pattern formation and evolution in coupled map lattices when advection is incorporate...
This paper is mainly concerned with a kind of coupled map lattices (CMLs). New definitions of dense ...
A new method for the identification of nonlinear Coupled Map Lattice (CML) equations from measured s...
This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and in...
It is investigated how a spatial quenched disorder modifies the dynamics of coupled map lattices. Th...
The paper presents a simple mathematical model called a coupled map lattice (CML). For some range of...
We prove that the attractor of the 1D quintic complex Ginzburg-Landau equation with a broken phase s...
. In this paper recent work on the dynamics of lattice differential equations is surveyed. In partic...
There has been revival of interest in Jerky flow from the point of view of dynamical systems. The ea...