Stacked Fronts for Cooperative Systems with Equal Diffusion Coefficients
Stacked Fronts for Cooperative Systems with Equal Diffusion Coefficients
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DOI：
10.1137/100792846
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
M. Iida;R. Lui;H. Ninomiya
中科院分区：
文献类型：
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作者：
M. Iida;R. Lui;H. Ninomiya
本文研究了具有等扩散系数的m分量合作系统。没有扩散的动力学系统具有$m+1$平衡，其中一个是稳定的，其他的，包括原点，是不稳定的。对于扩散-合作系统，人们可能认为从原点到稳定平衡的过渡导致了在Fisher-KPP方程中观察到的行进锋的形成。然而，这并不总是正确的。结果表明，在一定条件下，合作系统解的所有分量都以与Fisher-KPP方程相同的速度传播，而在其他条件下，某些分量的解不会发展成单一的波前.在这些后一种情况下，这些分量可能发展成堆叠的锋，其中每个锋以与其他锋不同的速度传播。
In this paper m-component cooperative systems with equal diffusion coefficients are considered. The kinetic system without diffusion possesses $m+1$ equilibria where one is stable and the others, including the origin, are unstable. For the diffusion-cooperative system, one might think that the transition from the origin to the stable equilibrium causes the formation of traveling fronts as observed in the Fisher-KPP equation. However, this is not always true. It is shown that under certain conditions all components of the solutions of the cooperative system propagate at the same speed as seen in the Fisher-KPP equation, while under certain other conditions some components of the solutions do not develop into single traveling fronts. In these latter cases those components may develop into stacked fronts where each front propagates at a different speed than the others.