We address the uniqueness of the nonzero stationary state for a reaction–diffusion system of Fisher–KPP type that does not satisfy the comparison principle. Although the uniqueness is false in general, it turns out to be true under biologically natural assumptions on the parameters. This Liouville-type result is then used to characterize the wake of traveling waves. All results are extended to an analogous nonlocal reaction–diffusion equation that contains as a particular case the cane toads equation with bounded traits.

中文翻译：

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非合作Fisher-KPP系统和圆柱非局部方程的Liouville型结果

我们针对不满足比较原理的Fisher-KPP类型的反应扩散系统，解决了非零稳态的唯一性。尽管唯一性通常是错误的，但在对参数的生物学自然假设下，事实证明它是正确的。然后将该Liouville型结果用于表征行波的苏醒。所有结果都扩展到一个类似的非局部反应扩散方程，在特定情况下，该方程包含具有有限性状的甘蔗蟾蜍方程。