期刊
JOURNAL OF MATHEMATICAL BIOLOGY
卷 53, 期 4, 页码 617-641出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-006-0013-2
关键词
reaction-diffusion systems; cross-diffusion systems; Turing's instability
The cross-diffusion competition systems were introduced by Shigesada et al. [J. Theor. Biol. 79, 83-99 (1979)] to describe the population pressure by other species. In this paper, introducing the densities of the active individuals and the less active ones, we show that the cross-diffusion competition system can be approximated by the reaction-diffusion system which only includes the linear diffusion. The linearized stability around the constant equilibrium solution is also studied, which implies that the cross-diffusion induced instability can be regarded as Turing's instability of the corresponding reaction-diffusion system.
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