We consider the well-known Bazykin–Svirezhev model describing the predator–prey interaction. This model is a system of two nonlinear ordinary differential equations with a small parameter multiplying one of the derivatives. The existence and stability of a so-called relaxation cycle in such a system are studied. A peculiar feature of such a cycle is that as the small parameter tends to zero, its fast component changes in a $$\delta $$ -like manner, while the slow component tends to some discontinuous periodic function.

中文翻译：

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数学捕食者-猎物模型中的非经典松弛振荡

我们考虑描述捕食者-猎物相互作用的著名 Bazykin-Svirezhev 模型。该模型是一个由两个非线性常微分方程组成的系统，其中一个小参数乘以一个导数。研究了这种系统中所谓弛豫循环的存在性和稳定性。这种循环的一个特点是，当小参数趋于零时，它的快分量以类似 $$\delta $$ 的方式变化，而慢分量则趋向于一些不连续的周期函数。