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Dynamic Complexity of an Ivlev‐Type Prey‐Predator System with Impulsive State Feedback Control

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  • Chuanjun Dai
  • Min Zhao
  • Lansun Chen

Abstract

The dynamic complexities of an Ivlev‐type prey‐predator system with impulsive state feedback control are studied analytically and numerically. Using the analogue of the Poincaré criterion, sufficient conditions for the existence and the stability of semitrivial periodic solutions can be obtained. Furthermore, the bifurcation diagrams and phase diagrams are investigated by means of numerical simulations, which illustrate the feasibility of the main results presented here.

Suggested Citation

  • Chuanjun Dai & Min Zhao & Lansun Chen, 2012. "Dynamic Complexity of an Ivlev‐Type Prey‐Predator System with Impulsive State Feedback Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:534276
    DOI: 10.1155/2012/534276
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    References listed on IDEAS

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    1. Wen-Zhen Gong & Qiongfen Zhang & X. H. Tang, 2012. "Existence of Subharmonic Solutions for a Class of Second‐Order p‐Laplacian Systems with Impulsive Effects," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Ileana Miranda Cabrera & Heyker Lellanis Baños Díaz & María de los Ángeles Martínez, 2010. "Dynamical System and Nonlinear Regression for Estimate Host‐Parasitoid Relationship," Journal of Applied Mathematics, John Wiley & Sons, vol. 2010(1).
    3. Scott A. Hadley & Lawrence K. Forbes, 2009. "Dynamical Systems Analysis of a Five‐Dimensional Trophic Food Web Model in the Southern Oceans," Journal of Applied Mathematics, John Wiley & Sons, vol. 2009(1).
    4. Fengde Chen, 2005. "Periodicity in a ratio‐dependent predator‐prey system with stage structure for predator," Journal of Applied Mathematics, John Wiley & Sons, vol. 2005(2), pages 153-169.
    5. Zhang, Limin & Zhao, Min, 2009. "Dynamic complexities in a hyperparasitic system with prolonged diapause for host," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1136-1142.
    6. Fengde Chen, 2005. "Periodicity in a ratio-dependent predator-prey system with stage structure for predator," Journal of Applied Mathematics, Hindawi, vol. 2005, pages 1-17, January.
    7. 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.
    8. Scott A. Hadley & Lawrence K. Forbes, 2009. "Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans," Journal of Applied Mathematics, Hindawi, vol. 2009, pages 1-17, February.
    9. Ileana Miranda Cabrera & Heyker Lellanis Baños Díaz & María de los Ángeles Martínez, 2010. "Dynamical System and Nonlinear Regression for Estimate Host-Parasitoid Relationship," Journal of Applied Mathematics, Hindawi, vol. 2010, pages 1-10, November.
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    Cited by:

    1. Chuanjun Dai & Min Zhao & Lansun Chen, 2013. "Bifurcations and Periodic Solutions for an Algae‐Fish Semicontinuous System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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