Qualitative analysis and chaos control in a density-dependent host–parasitoid system

Abstract

We study the comprehensive dynamics of a density-dependent host–parasitoid system with the Hassell growth function for the host population. Particularly, we investigate the dynamical properties related to boundedness, local asymptotic stability of boundary equilibrium, existence and uniqueness of positive equilibrium point and global asymptotic stability of the positive equilibrium point of this modified host–parasitoid model. Moreover, it is also proved both populations endure period-doubling bifurcation and Neimark–Sacker bifurcation at positive steady-state with suitable choice of parametric values. OGY method is implemented in order to controlling chaos in host–parasitoid model. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behavior in the model.