关于一类害虫治理流行病Filippov模型的动力学性质分析

Dynamic Analysis of an Epidemic Filippov Model on Pest Control

首先,在不采取综合害虫治理策略的情况下,本文给出一个具有流行病的害虫模型的正平衡点的存在条件以及无病平衡点和正平衡点的全局稳定性条件;其次,把易感害虫种群数量作为害虫综合控制的指标,利用阈值控制策略建立了一个害虫治理流行病Filippov模型,并系统地对该模型的动力学性质进行分析,其中包括模型的滑线区域,真、假平衡点及伪平衡点的存在性和稳定性.

In this paper, we first investigate the conditions of the existence of positive equilibria and the global stability of infection-free and positive equilibria without Integrated Pest Management strategy. Secondly, considering the susceptible pest populations as the index of pest control, we establish an epidemic Filippov model by using threshold control strategy and system- atically analyze the dynamics of such a system including sliding region, real and virtual equilibria, existence conditions and stability of pseudo equilibrium.