Cross-diffusion-driven instability in a reaction-diffusion Harrison predator-prey model
type: Item
instance of: scholarly article
title: Cross-diffusion-driven instability in a reaction-diffusion Harrison predator-prey model
zbMATH Open document ID: 1402.92374
DOI: 10.1155/2013/306467
author: Xiaoqin Wang
author: Yongli Cai
published in: Abstract and Applied Analysis
publication date: 2013-05-08T00:00:00Z
review text: Summary: We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing's instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences ``spots \(\rightarrow \) spot-stripe mixtures \(\rightarrow\) stripes \(\rightarrow\) hole-stripe mixtures \(\rightarrow \) holes'' are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 6161320
zbMATH Keywords: population with cross-diffusion
zbMATH Keywords: Harrison-type predator-prey model
zbMATH Keywords: Turing's instability
describes a project that uses: PRED_PREY
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/306467
OpenAlex ID: W2015989271
Wikidata QID: Q58915885
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description: scientific article; zbMATH DE number 6161320