中国物理B ›› 2008, Vol. 17 ›› Issue (11): 3936-3941.doi: 10.1088/1674-1056/17/11/003

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Pattern formation induced by cross-diffusion in a predator--prey system

靳 祯2, 刘权兴3, 李 莉3   

  • 收稿日期:2008-03-24 修回日期:2008-04-11 出版日期:2008-11-20 发布日期:2008-11-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60771026), Program for New Century Excellent Talents in University of China (Grant No NCET050271), and the Special Scientific Research Foundation for the Subjects of Doctors in University of China (Grant No 20060110005).

Pattern formation induced by cross-diffusion in a predator--prey system

Sun Gui-Quan (孙桂全), Jin Zhen(靳祯), Liu Quan-Xing(刘权兴), Li Li(李莉)   

  1. Department of Mathematics, North University of China, Taiyuan 030051, China
  • Received:2008-03-24 Revised:2008-04-11 Online:2008-11-20 Published:2008-11-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60771026), Program for New Century Excellent Talents in University of China (Grant No NCET050271), and the Special Scientific Research Foundation for the Subjects of Doctors in University of China (Grant No 20060110005).

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摘要： This paper considers the Holling--Tanner model for predator--prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients. However, combined with cross-diffusion, it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations. Furthermore, asynchrony of the predator and the prey in the space. The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator--prey system.

关键词: Holling--Tanner, cross-diffusion, pattern structures

Abstract: This paper considers the Holling--Tanner model for predator--prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients. However, combined with cross-diffusion, it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations. Furthermore, asynchrony of the predator and the prey in the space. The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator--prey system.

Key words: Holling--Tanner, cross-diffusion, pattern structures

中图分类号:  (Population dynamics and ecological pattern formation)

  • 87.23.Cc
89.75.Kd (Patterns)