On slow–fast dynamics in a classical predator–prey system

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.