Diffusion, Cross-diffusion and Competitive Interaction
Diffusion, Cross-diffusion and Competitive Interaction
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DOI：
10.1007/s00285-006-0013-2
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发表时间：
2006-06
影响因子：
1.9
通讯作者：
M. Iida;M. Mimura;H. Ninomiya
中科院分区：
文献类型：
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作者：
M. Iida;M. Mimura;H. Ninomiya
交叉扩散竞争系统由Shigesada等人提出[J]。定理。生物学报，79,83-99(1979)]来描述其他物种的种群压力。本文通过引入活跃个体和不活跃个体的密度，证明了交叉扩散竞争系统可以用只包含线性扩散的反应扩散系统来近似。研究了在恒定平衡解附近的线性化稳定性，表明交叉扩散引起的不稳定性可以看作是相应反应扩散系统的图灵不稳定性。
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.