A Predator-Prey System with Mutual Interference Concerning IPM

Abstract

A predator-prey system with mutual interference concerning Integrated Pest Management (IPM) is considered. The locally stable prey-eradication periodic solution is obtained when the impulsive period is less than some critical value by using Floquet theorem and small amplitude perturbation skills. Otherwise, the system is permanent. Numerical examples show that the system considered has more complicated dynamics behaviors, such as: (1) high-order periodic oscillation, (2) period-doubling bifurcation, (3) symmetry-breaking bifurcation, (4) attractor crisis, etc. Finally, some conclusions are given.