舞毒蛾非线性模型及其动态

NONLINEAR MODEL FOR GYPSY MOTH AND ITS DYNAMICS

从森林-舞毒蛾-寄生天敌系统的相互作用机理出发，组建了描述这个系统动力学行为的非线性离散模型：F_(t+1)=F_tcxp(r-r(F_t+bcG_t)/K),G_(t+1)=sG_texp(m(aF-cG)/K-qP_t,P_(t-1)=wG_t(1-exP(1-qP_t))讨论了模型的平衡态及其稳定性以及舞毒蛾的非线性动力学行为．分析和模拟结果与舞毒蛾的动态行为是一致的．同时通过对模型的时间动态以及各参数变化对模型动态的影响进行的分析，发现参数a，s和c对爆发期的密度影响较大，而参数q和w对周期长短的作用较大，加深了对森林舞毒蛾天敌系统的认识，并为这个系统的调控提供理论依据．

A nonlinear discrete model to describe the dynamics of Gypsy moth population was developed awarding to the interaction among the systems of stand-Gypsy moth-parasitoid: The existence and stability of the model equilibrium were studied. The nonlinear dynamics of the Gypsy moth population was simulated. The results of the model are consistent with the real dynamics of the Gypsy moth population. Meanwhile, the time dynamics of the model and the effect of the parameter variation on the model reveal that, the parameters a, s and c have much influence on the density of the breakout and parameters q and w have influence on the period. This gives us deep understanding of the system and provides a theoretical accordance for the control on the system.