A new geometrical criterion for the transition to spatio-temporal chaos (STC) arising in the
Gray–Scott model is presented. This is based on the inter-relationship of global bifurcating …

Topological characterization of spatial-temporal chaos Page 1 Topological characterization of
spatial-temporal chaos Marcio Gameiro* and Konstantin Mischaikow † School of Mathematics …

Abstract In the Gray–Scott reaction–diffusion system one reactant is constantly fed in the
system, another reactant is reproduced by consuming the supplied reactant and also …

I show stable, localized, single and multi-spot patterns of three classes-stationary, moving,
and rotating-that exist within a limited range of parameter values in the two-dimensional …

The purpose of the research is to find the numerical solutions to the system of time
dependent nonlinear parabolic partial differential equations (PDEs) utilizing the Modified …

In this paper a method to rigorously compute several non trivial solutions of the Gray-Scott
reaction-diffusion system defined on a 2-dimensional bounded domain is presented. It is …

We study the finite-element nonlinear Galerkin method in one spatial dimension and its
application to the numerical solution of nontrivial dynamics in selected reaction–diffusion …

Abstract We consider the Gray–Scott model for cubic autocatalysis. We prove nonexistence
results on stationary and travelling pulse solutions for some domain of parameters. We …

Motivated by studies of the Greenberg-Hastings cellular automata (GHCA) as a caricature of
excitable systems, in this paper we study kink-antikink dynamics in the perhaps simplest …

In attempts to manage spatiotemporal transient chaos in spatially extended systems, these
systems are often subjected to protocols that perturb them as a whole and stabilize globally …