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 τ is less than the critical value τmax⁡. Otherwise, the system can be permanent. Moreover, numerical results clearly show with the increase of the impulsive period τ, 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.