Spatial pattern formation of a ratio-dependent predator–prey model

doi:10.1088/1674-1056/19/9/090206

Abstract This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatially distributed population with diffusion in a Holling-III ratio-dependent predator–prey model, the sufficient conditions for diffusion-driven instability with Neumann boundary conditions are obtained. Furthermore, it presents novel numerical evidence of time evolution of patterns controlled by diffusion in the model, and finds that the model dynamics exhibits complex pattern replication, and the pattern formation depends on the choice of the initial conditions. The ideas in this paper may provide a better understanding of the pattern formation in ecosystems.

Keywords: ratio-dependent predator–prey model Holling III functional response diffusion-driven instability pattern formation

Received: 28 October 2009
Revised: 24 December 2009
Accepted manuscript online:

PACS:	0290
	0565

Fund: Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y7080041).

Cite this article:

Lin Wang(林望) Spatial pattern formation of a ratio-dependent predator–prey model 2010 Chin. Phys. B 19 090206

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Spatial pattern formation of a ratio-dependent predator–prey model

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