Abstract We study a classical predator–prey system with the assumption that the birth rate of the prey is small in comparison with the death rate of the predator. As a consequence, some solutions of the system might have a slow–fast structure. Using singular perturbation technique and various scalings, we construct an approximation for the solution. Although the explicit formula for the solution is available, the approximation we have constructed describes the time behavior more explicitly. Furthermore, we indicate a domain near an equilibrium where slow–fast dynamics is absent.

中文翻译：

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经典捕食者-猎物系统中的慢速动力学

摘要 我们研究了一个经典的捕食者-猎物系统，假设猎物的出生率与捕食者的死亡率相比较小。因此，系统的某些解决方案可能具有慢-快结构。使用奇异扰动技术和各种缩放，我们构建了解决方案的近似值。尽管解决方案的显式公式可用，但我们构建的近似值更明确地描述了时间行为。此外，我们指出了一个接近平衡的域，其中不存在慢-快动态。