Turing instability and pattern induced by cross-diffusion in a predator-prey system with Allee effect

Yahong Peng and Tonghua Zhang

Applied Mathematics and Computation, 2016, vol. 275, issue C, 1-12

Abstract: In this paper, we first propose a mathematical model for a spatial predator-prey system with Allee effect. And then by using the proposed model, we investigate the Turing instability and the phenomena of pattern formation. We show how cross-diffusion destabilizes the spatially uniform steady state. The method of multiple time scales is employed to derive the amplitude equations, which is the cubic Stuart-Landau equation in the supercritical case and the quintic in the subcritical case. Based on the amplitude equations, we obtain the asymptotic solutions of the model close to the onset of instability.

Keywords: Cross-diffusion; Pattern formation; Turing instability; Amplitude equation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:275:y:2016:i:c:p:1-12

DOI: 10.1016/j.amc.2015.11.067

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