We show that the Flaschka map, originally introduced to analyze the dynamics of the integrable Toda lattice system, is the inverse of a momentum map. We discuss the geometrical setting of the map and apply it to the generalized Toda lattice systems on semisimple Lie algebras, the rigid body system on Toda orbits, and to coadjoint orbits of semidirect products groups. In addition, we develop an ...

Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c 0 ∗ > such that for each c c∗ ≥ , the systems under consideration admit monotonic nondecreasing traveling waves.

Chaotic evolution of structures in Coupled map lattice driven by identical noise on each site is studied (a structure is a group of neighbouring lattice–sites for whom values of dynamical variable follow certain predefined pattern). Number of structures is seen to follow a power–law decay with length of the structure for a given noise–strength. A novel phenomenon, which we call stochas-tic cohe...

and Applied Analysis 3 This paper is organized as follows. In Section 2, we give some preliminaries including a comparison principle. Then we prove uniqueness of traveling wave with nonzero speed in Section 3. 2. Preliminaries The following lemma can be easily deduced from 1.5 and 1.6 . Lemma 2.1. Let {ui,j}i,j∈Z be a solution of 1.1 – 1.6 . If c > 0 < 0 , then ui,j t → 0 → 1 as t → ∞ and ui,j ...

We propose a model for co-evolving ecosystems that takes into account two levels of description of an organism, for instance genotype and phenotype. Performance at the macroscopic level forces mutations at the microscopic level. These, in turn, affect the dynamics of the macroscopic variables. In some regions of parameter space, the system self-organises into a state with localised activity and...

In this paper we propose a coupled-map lattice for modelling epidemic spread in a fuzzy setting. The presented model complies with the need for adequate modelling tools to describe and/or predict spatio-temporal phenomena, following the growing availability of spatio-temporal data. Furthermore, our approach does not rely on partial differential equations making it particularly suited to model e...

We present an approach to the investigation of the statistical properties of weakly coupled map lattices that avoids completely cluster expansion techniques. Although here it is implemented on a simple case we expect similar strategies to be applicable in a much larger class of situations.