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Stability Analysis of Predator‐Prey System with Fuzzy Impulsive Control

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  • Yuangan Wang

Abstract

Having attracted much attention in the past few years, predator‐prey system provides a good mathematical model to present the correlation between predators and preys. This paper focuses on the robust stability of Lotka‐Volterra predator‐prey system with the fuzzy impulsive control model, and Takagi‐Sugeno (T‐S) fuzzy impulsive control model as well. Via the T‐S model and the Lyapunov method, the controlling conditions of the asymptotical stability and exponential stability are established. Furthermore, the numerical simulation for the Lotka‐Volterra predator‐prey system with impulsive effects verifies the effectiveness of the proposed methods.

Suggested Citation

  • Yuangan Wang, 2012. "Stability Analysis of Predator‐Prey System with Fuzzy Impulsive Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:715497
    DOI: 10.1155/2012/715497
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    References listed on IDEAS

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    1. Xu, Jian & Pei, Lijun & Lu, Zhiqi, 2006. "Lyapunov stability for a class of predator–prey model with delayed nutrient recycling," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 173-181.
    2. Li, Dong & Wang, Shilong & Zhang, Xiaohong & Yang, Dan, 2009. "Impulsive control of uncertain Lotka–Volterra predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1572-1577.
    3. Zhengrong Xiang & Guoxin Chen, 2012. "Stability Analysis and Robust H∞ Control of Switched Stochastic Systems with Time‐Varying Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Liu, Bin & Chen, Guanrong & Teo, Kok Lay & Liu, Xinzhi, 2005. "Robust global exponential synchronization of general Lur’e chaotic systems subject to impulsive disturbances and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1629-1641.
    5. Zhengrong Xiang & Guoxin Chen, 2012. "Stability Analysis and Robust Control of Switched Stochastic Systems with Time-Varying Delay," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, May.
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