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

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

中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90206-090206.doi: 10.1088/1674-1056/19/9/090206

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

林望

College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China

收稿日期:2009-10-28 修回日期:2009-12-24 出版日期:2010-09-15 发布日期:2010-09-15
基金资助:
Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y7080041).

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

Lin Wang(林望)^†ger

College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China

Received:2009-10-28 Revised:2009-12-24 Online:2010-09-15 Published:2010-09-15
Supported by:
Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y7080041).

摘要/Abstract

摘要： 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.

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.

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

中图分类号:

0290

林望. Spatial pattern formation of a ratio-dependent predator–prey model[J]. 中国物理B, 2010, 19(9): 90206-090206.

Lin Wang(林望). Spatial pattern formation of a ratio-dependent predator–prey model[J]. Chin. Phys. B, 2010, 19(9): 90206-090206.

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

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

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