食饵具群体防卫效应和捕食者具阶段结构的脉冲控制捕食系统

A Prey with Group Defense and Predator with Stage-structure Prey-predator System Concerning Impulsive Control

本文研究一类捕食者具有阶段结构和食饵具有群体防卫作用的脉冲控制系统,应用Floquet乘子理论和脉冲比较定理,获得食饵(害虫)灭绝周期解局部稳定和系统持续生存的充分条件,并通过数值例子揭示了系统诸如高倍周期振荡,混沌,吸引子突变,倍周期与半周期分支等复杂的动力学现象.讨论脉冲周期,成年食饵的投放量和群体防卫效应系数对系统的重要作用,得出的结论为实际的害虫管理提供了可靠的策略依据.

A prey with group defense and predator with stage-structure prey-predator system concerning impulsive controlling is considered. The sufficient conditions for locally stable of prey-eradication periodic solution and permanence of the system are obtained,by using Floquet theorem and comparison theorem of impulsive differential equation. Numerical example show that the system considered has more complicated dynamics, such as high order periodic oscillating, chaos, attractor crisis, period-doubling and period-halving bifurcation, etc. The importance of the impulsive period,the released amount of mature predator and the coefficient of group defense effect are discussed. Our results provide reliable strategy basis for practical pest management.