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Dynamic analysis of a pest-epidemic model with impulsive control

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  • Pang, Guoping
  • Chen, Lansun

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.

Suggested Citation

  • Pang, Guoping & Chen, Lansun, 2008. "Dynamic analysis of a pest-epidemic model with impulsive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(1), pages 72-84.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:1:p:72-84
    DOI: 10.1016/j.matcom.2007.10.002
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    References listed on IDEAS

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    1. Sun, Jitao, 2004. "Impulsive control of a new chaotic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(6), pages 669-677.
    2. Sun, Jitao & Zhang, Yinping, 2004. "Impulsive control and synchronization of Chua’s oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 499-508.
    3. Hyakutake, Toru & Matsumoto, Takeshi & Yanase, Shinichiro, 2006. "Lattice Boltzmann simulation of blood cell behavior at microvascular bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 72(2), pages 134-140.
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    1. Pozna, Claudiu & Troester, Fritz & Precup, Radu-Emil & Tar, József K. & Preitl, Stefan, 2009. "On the design of an obstacle avoiding trajectory: Method and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2211-2226.

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