Diffusion, Cross-diffusion and Competitive Interaction
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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.
KeywordsReaction-diffusion systems Cross-diffusion systems Turing’s instability
Mathematics Subject Classification (2000)35B25 35K55 35K57
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