Appl. Math. Lett. | 2021
Relaxation oscillations for Leslie-type predator-prey model with Holling Type I response functional function
Abstract
Abstract This paper deals with a class of Leslie-type model with two characteristic time scales. Instead of the typically used analytic functional response function, we assume that the predator–prey system with Holling type I functional response function, which yield a piecewise smooth slow-fast system. Using geometry singular perturbation theory, we revealed that it can have exactly two relaxation oscillations, the inner one unstable and outer one stable. Numerical simulations for the coexistence of two relaxation oscillations are also given in support of the analytic results.