Dynamic complexity of a host–parasitoid ecological model with the Hassell growth function for the host

Abstract

This paper investigates a discrete-time host–parasitoid ecological model with Hassell growth function for the host by qualitative analysis and numerical simulation. Local stability analysis of the system is carried out. Many forms of complex dynamics are observed, including chaotic bands with periodic windows, pitchfork and tangent bifurcations, attractor crises, intermittency, supertransients, and non-unique dynamics (meaning that several attractors coexist). The largest Lyapunov exponents are numerically computed to confirm further the complexity of these dynamic behaviors.