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The Stability of Solutions for a Fractional Predator‐Prey System

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  • Yingjia Guo

Abstract

We study a class of fractional predator‐prey systems with Holling II functional response. A unique positive solution of this system is obtained. In order to prove the asymptotical stability of positive equilibrium for this system, we study the Lyapunov stability theory of a fractional system.

Suggested Citation

  • Yingjia Guo, 2014. "The Stability of Solutions for a Fractional Predator‐Prey System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:124145
    DOI: 10.1155/2014/124145
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    References listed on IDEAS

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    1. Zhenwen Liu & Ningzhong Shi & Daqing Jiang & Chunyan Ji, 2012. "The Asymptotic Behavior of a Stochastic Predator-Prey System with Holling II Functional Response," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, December.
    2. Lina Song & Weiguo Wang, 2013. "Solution of the Fractional Black‐Scholes Option Pricing Model by Finite Difference Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Lina Song & Weiguo Wang, 2013. "Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
    4. Zhenwen Liu & Ningzhong Shi & Daqing Jiang & Chunyan Ji, 2012. "The Asymptotic Behavior of a Stochastic Predator‐Prey System with Holling II Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Zhang, Shuwen & Chen, Lansun, 2005. "A Holling II functional response food chain model with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1269-1278.
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