Permanence and chaos in a host–parasitoid model with prolonged diapause for the host

The dynamic behavior of a host–parasitoid model with prolonged diapause for the host is investigated. It is proved that the system is permanent under certain appropriate conditions. Numerical simulations are presented to illustrate consistency with the theoretical analysis. For the biologically reasonable range of parameter values, the global dynamics of the system have been studied numerically. In particular, the effect of prolonged diapause on the system has been investigated. Many forms of complex dynamics are observed, including quasi-periodicity, period-doubling and period-halving bifurcations, chaotic bands with periodic windows, attractor crises, intermittency, and supertransients. These complex dynamic behaviors are confirmed by the largest Lyapunov exponents.