Pattern formation in a cross-diffusive Holling-Tanner model
type: Item
instance of: scholarly article
title: Pattern formation in a cross-diffusive Holling-Tanner model
zbMATH Open document ID: 1257.92012
DOI: 10.1155/2012/828219
author: Yanyan Li
published in: Discrete Dynamics in Nature and Society
publication date: 2013-02-21T00:00:00Z
review text: Summary: We present a theoretical analysis of the processes of pattern formation that involves organisms distributions and their interactions of spatially distributed populations with self- as well as cross-diffusion in a Holling-Tanner predator-prey model; sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained; and Hopf and Turing bifurcations in a spatial domain are presented, too. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- as well as cross-diffusion in the model, and find that the model dynamics exhibit a cross-diffusion controlled formation growth not only to spots, but also to strips, holes, and stripes-spots replications. The methods and results in the present paper may be useful for the research of pattern formations in the cross-diffusive models.
Mathematics Subject Classification ID: 92C15
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 6137753
Wikidata QID: Q58700781
describes a project that uses: PRED_PREY
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/828219
OpenAlex ID: W2006132755
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description: scientific article; zbMATH DE number 6137753