一类脉冲L-V系统的周期解和全局渐近性质

The Periodic Solutions and Globally Asymptotic Properties of L-V System with Impulsive Effects

研究了一类具有脉冲的周期L-V系统,利用脉冲微分方程的比较原理、Floquet理论及分析技巧,分析了系统周期解的存在性及系统解的全局渐近性质.并将所得到的一般结果应用于一类捕食-被捕食系统,获得了该系统正周期解的存在唯一及全局吸引的条件,进一步讨论了系统中种群灭绝的有关性质,给出一个实例进行数值模拟,阐明了所获得的理论结果。

In this paper, a class of periodic L-V impulsive system is studied. The comparison principle of impulsive differential equation, Floquet theory and some analysis techniques are used to analyse the exist- ence of the system periodic solution and global asymptotic properties of the system. Furthermore, the gen- eral results obtained are applied to a predator-prey system, so as to obtain the existence and uniqueness of positive periodic solution to the system. Some relevant nature of extinction of population species is further discussed. Also, this paper presents a practical example to carry out the numerical simulation and to illustrate the obtained theoretical results.