Relaxation oscillations in a class of predator-prey systems.
We consider a class of three-dimensional, singularly perturbed predator-prey systems having two predators competing exploitatively for the same prey in a constant environment. By using dynamical system techniques and the geometric singular perturbation theory, we give precise conditions which guarantee the existence of stable relaxation oscillations for systems within the class. Such result shows the coexistence of the predators and the prey with quite diversified time response which typically happens when the prey population grows much faster than those of predators. As an application, a well-known model is discussed in detail by showing the existence of stable relaxation oscillations for a wide range of parameter values of the model.
scientific article; zbMATH DE number 1891271