Coexistence states for a prey-predator model with cross-diffusion
type: Item
instance of: scholarly article
title: Coexistence states for a prey-predator model with cross-diffusion
zbMATH Open document ID: 1156.35318
author: Kousuke Kuto
author: Yoshio Yamada
published in: Discrete and Continuous Dynamical Systems
publication date: 2008-07-29T00:00:00Z
review text: The authors consider a Lotka-Volterra prey-predator interaction model with cross-diffusion. Using the linear contribution of the prey's growth rate as parameter, they show that the system admits two or three positive steady-state solutions, corresponding to different branches of a saddle node or pitchfork bifurcation. For these positive solutions the authors calculate the linear stability. They also find a Hopf bifurcation point on the steady state solution branch.
reviewed by: Alois Steindl
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5305463
zbMATH Keywords: cross-diffusion
zbMATH Keywords: steady-state solution
zbMATH Keywords: stability
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: Lotka-Volterra
zbMATH Keywords: saddle node or pitchfork bifurcation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5305463