Nonclassical Relaxation Oscillations in a Mathematical Predator-Prey Model

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.