Dynamics of a Hyperparasitic System with Prolonged Diapause for Host*
- 1 Department of Mathematics and Finance-Economics, Sichuan University of Arts and Science, Dazhou, China
- 2 School of International Trade and Economics, University of International Business and Economics, Beijing, China
Abstract
A hyperparasitic system with prolonged diapause for host is investigated. It is assumed that host prolonged diapause occur at larval stage, and parasitoid attack is limited to egg stage before the initiation of host diapause. Such behavior has been reported for many ichneumons. Hyperparasite only attack s the parasitoids that parasitize the hosts. Hyperparasitic system is often used in biological control. The existence and stability of nonnegative fixed points are explored. Numerical simulations are carried out to explore the global dynamics of the system, which demonstrate appropriate prolonged diapause rate and appropriate intrinsic growth rate can stabilize the system. The reasons are explained according to the ecological perspective. Furthermore, many other complexities which include quasi-periodicity, period-doubling bifurcations leading to chaos, chaotic attractor, intermittent and supertransients are observed.
- J. R. Beddington, C. A. Free and J. H. Lawton, “Dynamic Complexity in Predator-Prey Models Framed in Difference Equations,” Nature, Vol. 255, No. 5503, 1975, pp. 58-60. http://dx.doi.org/10.1038/255058a0
- S. Y. Tang and L. S. Chen, “Chaos in Functional Response Host-Parasitoid Esosystem Models,” Chaos, Solitons & Fractals, Vol. 13, No. 4, 2002, pp. 875-884. http://dx.doi.org/10.1016/S0960-0779(01)00063-7
- C. L. Xu and M. S. Boyce, “Dynamic Complexities in a Mutual Interference Host-Parasitoid Model,” Chaos, Solitons & Fractals, Vol. 24, No. 1, 2005, pp. 175-182.
- S. J. Lv and M. Zhao, “The Dynamic Complexity of a Host-Parasitoid Model with a Lower Bound for the Host,” Chaos, Solitons & Fractals, Vol. 36, No. 4, 2008, pp. 911-999. http://dx.doi.org/10.1016/j.chaos.2006.07.020
- L. Zhu and M. Zhao, “Dynamic Complexity of a HostParasitoid Ecological Model with the Hassell Growth Function for the Host,” Chaos, Solitons & Fractals, Vol. 39, No. 3, 2009, pp. 1259-1269. http://dx.doi.org/10.1016/j.chaos.2007.10.023
- M. Zhao and L. M. Zhang, “Permanence and Chaos in a Host-Parasitoid Model with Prolonged Diapause for the Host,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 12, 2009, pp. 4197-4203. http://dx.doi.org/10.1016/j.cnsns.2009.02.014
- M. Zhao, H. G. Yu and J. Zhu, “Effects of a Population Floor on the Persistence of Chaos in A Mutual Interference Host-Parasitoid Model,” Chaos, Solitons & Fractals, Vol. 42, No. 2, 2009, pp. 1245-1250. http://dx.doi.org/10.1016/j.chaos.2009.03.027
- M. Zhao, L. M. Zhang and J. Zhu, “Dynamics of a Host-Parasitoid Model with Prolonged Diapause for Parasitoid,” Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 1, 2011, pp. 455-462. http://dx.doi.org/10.1016/j.cnsns.2010.03.011
- E. G. Gu, “The Nonlinear Analysis on a Discrete HostParasitoid Model with Pesticidal Interference,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 6, 2009, pp. 2720-2727. http://dx.doi.org/10.1016/j.cnsns.2008.08.012
- S. Y. Tang, Y. N. Xiao and R. A. Cheke, “Multiple Attractors of Host-Parasitoid Models with Integrated Pest Management Strategies: Eradication, Persistence and Outbreak,” Theoretical Population Biology, Vol. 73, No. 2, 2008, pp. 181-197. http://dx.doi.org/10.1016/j.tpb.2007.12.001
- C. A. Cobbold, J. Roland and M. A. Lewis, “The Impact of Parasitoid Emergence Time on Host-Parasitoid Population Dynamics,” Theoretical Population Biology, Vol. 75, No. 2-3, 2009, pp. 201-215. http://dx.doi.org/10.1016/j.tpb.2009.02.004