Infinite dimensional relaxation oscillation in aggregation-growth systems
type: Item
instance of: scholarly article
title: Infinite dimensional relaxation oscillation in aggregation-growth systems
zbMATH Open document ID: 1263.35027
author: Hirofumi Izuhara
author: Masayasu Mimura
author: Shin-Ichiro Ei
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2012-09-12T00:00:00Z
review text: A three-component diffusion-growth system with two-mode dispersion and a two-component cross-diffusion system are introduced. These models are motivated by pheromone-driven aggregation. The cross-diffusion model is derived as a formal limit of the diffusion-growth model. For both models bifurcation diagrams are obtained for decreasing intrinsic growth rates \(\delta\). In particular, for small \(\delta\) oscillatory solutions emerge. If \(\delta\) is sufficiently small, the existence of infinite-dimensional relaxation-oscillation consisting of fast and slow dynamics is proved under appropriate assumptions.
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 6081726
zbMATH Keywords: two-mode dispersion
zbMATH Keywords: two-component cross-diffusion
zbMATH Keywords: bifurcation diagrams
zbMATH Keywords: fast and slow dynamics
MaRDI profile type: Publication
full work available at URL: dcdsb.2012.17.1859
OpenAlex ID: W2314749288
DOI: 10.3934/DCDSB.2012.17.1859
description: scientific article; zbMATH DE number 6081726