In this short note, we study the Fisher-KPP population model with a time-dependent Allee threshold. We consider the time dependence as sinusoidal functions and rational functions as they relate to varying environmental situations of the model. Employing the generalized Riccati equation mapping method, we obtain exact traveling wave solutions. Also, when the time-dependent Allee threshold decays to a constant value, we recover the traveling wave solution of the degenerate Fitzhugh-Nagumo equation from our general solution.

中文翻译：

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具有时间依赖性Allee效应的Fisher-KPP方程的分析

在本简短说明中，我们研究具有时间依赖性Allee阈值的Fisher-KPP人口模型。我们将时间依赖性视为正弦函数和有理函数，因为它们与模型的变化环境有关。利用广义Riccati方程映射方法，我们获得了精确的行波解。同样，当与时间有关的Allee阈值衰减到一个恒定值时，我们将从一般解中恢复退化的Fitzhugh-Nagumo方程的行波解。