Stacked Fronts for Cooperative Systems with Equal Diffusion Coefficients

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.