Dynamic analysis of a pest-epidemic model with impulsive control

Guoping Pang and Lansun Chen

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 1, 72-84

Abstract: 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.

Keywords: Pest-epidemic model; Impulsive control; Extinction; Permanence; Chaos (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:1:p:72-84

DOI: 10.1016/j.matcom.2007.10.002

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