Analytical bifurcation behaviors of a host–parasitoid model with Holling type III functional response

Abstract This topic presents a study on host–parasitoid model with Holling type III functional response. In population dynamics, when host density rises, the parasitoid response initially accelerates due to parasitoid’s improved searching efficiency. However, above certain threshold, will reach saturation level influence of reducing handling time. Thus, we incorporated into characterize such phenomenon. The dynamics current are discussed in this paper. We first obtained existence and local stability conditions positive fixed point model. Furthermore, investigated bifurcation behaviors at point. More specifically, used theory center manifold theorem prove that possess both period doubling Neimark–Sacker bifurcations. Then, chaotic behavior model, sense Marotto, is proven. apply state-delayed feedback control strategy complex present Finally, numerical examples provided support our analytic results.