Pattern formation induced by cross-diffusion in a predator--prey system |
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Authors: | Sun Gui-Quan Jin Zhen Liu Quan-Xing and Li Li |
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Institution: | Department of Mathematics, North University of China, Taiyuan 030051, China |
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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. |
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Keywords: | Holling--Tanner cross-diffusion pattern structures |
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