具功能反应的脉冲食饵两捕食者系统的分支与混沌

Bifurcation and chaos of a one-prey two-predator impulsive system with functional response

文章基于害虫综合管理策略,利用脉冲比较定理、Floquent理论及微小扰动法,研究了具有功能反应、脉冲比例收获和脉冲常数投放的食饵两捕食者系统的分支与混沌,给出了投放临界值p*2,得到了系统灭绝和持续生存的充分条件,最后讨论了该生物综合管理策略的有效性。数值模拟表明,随着投放量p2的增加,系统出现倍周期分支、对称破裂分支、混沌、半周期分支、吸引子突变等复杂的动力学性质。

In this paper, a class of prey-predator systems with functional response, impulsive ratio harvest and impulsive release is established by the strategy of integrated pest management. The critical value p2^＊ of impulsive immigration and sufficient conditions for the system to be extinct Or sustainable are given by using the impulsive comparison theorem, Floquent theory and small amplitude perturbation skill. Numerical simulations show that with the increasing of immigration P2 the system has more Complex dynamics including periodic doubling bifurcation, symmetry-breaking bifurcation, chaos, periodic halving bifurcation, crises, etc. It is pointed out that the strategy of integrated pest management is more effective than the classical one.