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Dynamical Analysis of a Pest Management Model with Saturated Growth Rate and State Dependent Impulsive Effects

Author

Listed:
  • Wencai Zhao
  • Tongqian Zhang
  • Xinzhu Meng
  • Yang Yang

Abstract

A new pest management mathematical model with saturated growth is proposed. The integrated pest management (IPM) strategy by introducing two state dependent pulses into the model is considered. Firstly, we analyze singular points of the model qualitatively and get the condition for focus point. Secondly, by using geometry theory of impulsive differential equation, the existence and stability of periodic solution of the system are discussed. Lastly, some examples and numerical simulations are given to illustrate our results.

Suggested Citation

  • Wencai Zhao & Tongqian Zhang & Xinzhu Meng & Yang Yang, 2013. "Dynamical Analysis of a Pest Management Model with Saturated Growth Rate and State Dependent Impulsive Effects," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:204642
    DOI: 10.1155/2013/204642
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    References listed on IDEAS

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    1. Tongqian Zhang & Xinzhu Meng & Yi Song & Zhenqing Li, 2012. "Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Nie, Linfei & Teng, Zhidong & Hu, Lin & Peng, Jigen, 2009. "Existence and stability of periodic solution of a predator–prey model with state-dependent impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2122-2134.
    3. Tongqian Zhang & Xinzhu Meng & Yi Song & Zhenqing Li, 2012. "Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, April.
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