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Analysis of a Periodic Single Species Population Model Involving Constant Impulsive Perturbation

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Listed:
  • Ronghua Tan
  • Zuxiong Li
  • Shengliang Guo
  • Zhijun Liu

Abstract

This is a continuation of the work of Tan et al. (2012). In this paper a periodic single species model controlled by constant impulsive perturbation is investigated. The constant impulse is realized at fixed moments of time. With the help of the comparison theorem of impulsive differential equations and Lyapunov functions, sufficient conditions for the permanence and global attractivity are established, respectively. Also, by comparing the above results with corresponding known results of Tan et al. (2012) (i.e., the above model with linear impulsive perturbations), we find that the two different types of impulsive perturbations have influence on the above dynamics. Numerical simulations are presented to substantiate our analytical results.

Suggested Citation

  • Ronghua Tan & Zuxiong Li & Shengliang Guo & Zhijun Liu, 2014. "Analysis of a Periodic Single Species Population Model Involving Constant Impulsive Perturbation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:186232
    DOI: 10.1155/2014/186232
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    References listed on IDEAS

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    1. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2005. "New stability conditions for neural networks with constant and variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1391-1398.
    2. Chen, Huabin, 2010. "Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 50-56, January.
    3. Zhang, Hongbin & Li, Chunguang & Liao, Xiaofeng, 2005. "A note on the robust stability of neural networks with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 357-360.
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