Mathematical models of population interactions with dispersal. II: Differential survival in a change of habitat
type: Item
instance of: scholarly article
title: Mathematical models of population interactions with dispersal. II: Differential survival in a change of habitat
zbMATH Open document ID: 0588.92020
DOI: 10.1016/0022-247X(86)90029-6
author: Bindhyachal Rai
author: Paul Waltman
author: H. I. Freedman
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: [For part I see SIAM J. Appl. Math. 32, 631-648 (1977; Zbl 0362.92006).] - The paper considers a model of dispersing populations in the form of a system of nonlinear ordinary differential equations. Dispersal pressure is density dependent and a parameter measures the barrier strength. The model also incorporates a transition probability to allow for a risk in changing habitats. For the two-dimensional case, the region in parameter space for existence of a stable equilibrium solution is exactly determined, bounded in part by a branch of a hyperbola. For the n-dimensional case, similar, but less complete results are obtained.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 3945947
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: dispersing populations
zbMATH Keywords: nonlinear ordinary differential equations
zbMATH Keywords: Dispersal pressure
zbMATH Keywords: barrier strength
zbMATH Keywords: transition probability
zbMATH Keywords: risk in changing habitats
zbMATH Keywords: existence of a stable equilibrium solution
MaRDI profile type: Publication
cites work: Migratory effects in predator-prey models
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cites work: Dynamics of a single species in a spatially varying environment: The stabilizing role of high dispersal rates
cites work: Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution
cites work: Q4106027
description: scientific article; zbMATH DE number 3945947