Relaxation autowaves
type: Item
instance of: scholarly article
title: Relaxation autowaves
zbMATH Open document ID: 1190.34052
DOI: 10.1134/S0012266109060020
published in: Differential Equations
publication date: 2009-10-08T00:00:00Z
review text: This paper is a first step in the use of underlying ideas of the theory of relaxation oscillations in ordinary differential equations as a tool that can help to understand the intrinsic essence of self-organization modes in reaction-diffusion systems. The paper deals with a bilocal model of the classical Hutchinson equation with diffusion and with large Malthusian parameter of linear growth. First, the author develops a method for constructing the asymptotics of the relaxation Hutchinson cycle with arbitrary accuracy. Then, for appropiate values of the migration constant and the Malthusian parameter, and choosing the initial values of the population in a suitable space, a Poincaré map can be defined so that the corresponding periodic solution can be referred to as the self-organization mode of the considered Hutchinson system.
reviewed by: Eva Sánchez
Mathematics Subject Classification ID: 34C26
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5611085
zbMATH Keywords: Hutchinson equation
zbMATH Keywords: self-organization mode
zbMATH Keywords: relaxation cycle
author: Ju. S. Kolesov
MaRDI profile type: Publication
cites work: Q4884302
cites work: Q4864744
cites work: Q4318853
full work available at URL: s0012266109060020
OpenAlex ID: W3187611715
description: scientific article; zbMATH DE number 5611085