Dynamic complexities in a hyperparasitic system with prolonged diapause for host

In this paper, a hyperparasitic system with prolonged diapause for host is proposed and analyzed. For the biologically reasonable range of parameter values, the global dynamics of the system has been studied numerically. Especially, the effect of prolonged diapause and hyperparasitism on the system is investigated. Many forms of complex dynamics are observed. The complexities include (1) chaotic bands with periodic windows; (2) antimonotonicity; (3) pitchfork and tangent bifurcations; (4) period-doubling cascades; (5) intermittency; (6) supertransients; (7) non-unique dynamic, meaning that several attractors coexist; and (8) attractors crises. Furthermore, the complex dynamic behaviors of the model are confirmed by the largest Lyapunov exponents.