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.
Received: 24 March 2008
Revised: 11 April 2008
Accepted manuscript online:
PACS:
87.23.Cc
(Population dynamics and ecological pattern formation)
Fund: 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).
Cite this article:
Sun Gui-Quan (孙桂全), Jin Zhen(靳 祯), Liu Quan-Xing(刘权兴), Li Li(李莉) Pattern formation induced by cross-diffusion in a predator--prey system 2008 Chin. Phys. B 17 3936
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