Open Access
2013 Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model
Xiaoqin Wang, Yongli Cai
Abstr. Appl. Anal. 2013(SI36): 1-9 (2013). DOI: 10.1155/2013/306467


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 → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.


Download Citation

Xiaoqin Wang. Yongli Cai. "Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model." Abstr. Appl. Anal. 2013 (SI36) 1 - 9, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 06161320
MathSciNet: MR3034881
Digital Object Identifier: 10.1155/2013/306467

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI36 • 2013
Back to Top