Transient Dynamics in Fast–Slow Predator–Prey Model with Monod–Haldane Functional Response and Asymptotic Behaviors

Abstract

This paper studies the transient dynamics in a fast–slow ecological model with a Monod–Haldane functional response. Geometric singular perturbation theory is utilized to examine the transient dynamics generated by intrinsic multiple time scales. An asymptotic series solution is derived for the normally hyperbolic sub-manifold in the slow flow. The paper proves the existence of relaxation oscillations near fold points and the existence of a smooth family of canard cycles arising from folded singularities. Furthermore, it investigates the resulting canard explosion and transient dynamics numerically. By incorporating the Monod–Haldane functional response, which represents the inhibitory effect on predation at high prey population levels, this study illustrates the occurrence of transient dynamics under this mechanism.