Find in Library

We consider fast-slow planar systems of predator–prey models with the prey growing much faster than the predator. By using basic differential and integral calculus, Lyapunov functions and phase plane analysis, other than the geometric singular perturbation theory, we derive that the limit cycle exhibits the temporal pattern of a stable relaxation oscillator as a parameter tends to 0, such result shows the coexistence of the predator and the prey with quite diversified time response, which typically happens when the prey population grows much faster than those of predator.