Dynamic analysis of a pest-epidemic model with impulsive control
Based on biological control strategy in pest management, we construct and investigate a pest-epidemic model with impulsive control, i.e., periodic spraying microbial pesticide and releasing infected pests at different fixed moments. By using Floquet theorem and comparison theorem. we prove that the pest-eradication periodic solution is globally asymptotically stable when the impulsive period tau is less than the critical value tau(max). Otherwise, the system can be permanent. Moreover, numerical results clearly show with the increase of the impulsive period tau. the system exhibits a wide variety of dynamic behaviors including a sequence of direct and inverse cascade of periodic-doubling. symmetry-breaking pitchfork bifurcation, chaos and non-unique dynamics. which implies that the impulsive effect makes the dynamic behavior of the system more complex. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.
pest-epidemic model impulsive control permanence chaos extinction