一类慢变Filippov捕食-被捕食系统的分岔机理分析  

Bifurcation Analysis of a Class of Filippov Predator-Prey System with Slow Variable

作　　者：李静 张正娣[1] 彭淼 曲子芳[1] LI Jing, ZHANG Zheng-di, PENG Miao, QU Zi-fang(Faculty of Science, Jiangsu University, Zhenjiang 212013, Chin)

机构地区：[1]江苏大学理学院

出　　处：《数学的实践与认识》2018年第17期314-320,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金项目(11472116);国家自然科学基金重点项目(11632008);江苏省研究生科研与实践创新计划项目(5561190004,4061190009)

摘　　要：研究了生态学中含控制策略项的一类Filippov捕食-被捕食系统,由于害虫的环境容纳量受外界环境因素的影响而变化,故将害虫的环境容纳量视为周期慢变量,当慢变量的频率与系统的固有频率存在量级差异时,使得该Filippov捕食-被捕食系统体现出两时间尺度效应.通过将周期演变的环境容纳量视为控制参数,针对相应的广义自治系统,进行了平衡点的稳定性与分岔分析.借助于快慢分析法、微分包含理论,得到了在典型参数条件下,系统展现的一些特殊分岔模式,并对相关的机理予以了解释,由此丰富了对该类Filippov捕食-被捕食系统的研究.This paper studies a Filippov predator-prey system with control strategy in Ecology. Since the carrying capacity of the prey is influenced by the external environment factors, we regard it as a periodic slow variable, which leads an order gap between the exciting frequency and the natural frequency, thus the Filippov predator-prey system contains two time scales effect. By taking the environmental capacity of the periodic solution as the control parameter, the stability and bifurcation analysis of the equilibrium point is carried out for the corresponding generalized autonomous system. By means of fast-slow analysis and Filippov＇ s convex method, some special bifurcation types can be observed, due to the two cases of conversion rate. Meanwhile, related dynamic mechanisms are explained, which enrich the researches on this kind of Filippov predator-prey system.

关 键 词：Filippov捕食-被捕食系统 经济阈值 两时间尺度 滑动分岔 机理分析 

分 类 号：O175[理学—数学]