In this note, we deal with a model of population dynamics with memory effects subject to instantaneous external actions. We interpret the model as an impulsive Cauchy problem driven by a semilinear differential equation with functional delay. The existence of delayed impulsive solutions to the Cauchy problem leads to the presence of hereditary impulsive dynamics for the model. Furthermore, using the same procedure we study a nonlinear reaction–diffusion model.

中文翻译：

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脉冲效应下的遗传进化过程

在本说明中，我们处理的是种群动态模型，该模型具有受瞬时外部作用影响的记忆效应。我们将模型解释为由具有功能延迟的半线性微分方程驱动的脉冲柯西问题。Cauchy问题的延迟脉冲解的存在导致了模型的遗传脉冲动力学的存在。此外，使用相同的程序，我们研究了非线性反应扩散模型。