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Stability and Hopf bifurcation analysis in a prey–predator system with stage-structure for prey and time delay

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  • Chen, Yuanyuan
  • Changming, Song

Abstract

A delay-differential modelling with stage-structure for prey is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation theory, and its linear stability and Hopf bifurcation are demonstrated by studying the characteristic equation. The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold argument, and numerical simulations are given to illustrate the analytical result.

Suggested Citation

  • Chen, Yuanyuan & Changming, Song, 2008. "Stability and Hopf bifurcation analysis in a prey–predator system with stage-structure for prey and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1104-1114.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:1104-1114
    DOI: 10.1016/j.chaos.2007.01.035
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    References listed on IDEAS

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    1. 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.
    2. Rui Xu & M. A. J. Chaplain & F. A. Davidson, 2004. "Periodic solutions of a delayed predator-prey model with stage structure for predator," Journal of Applied Mathematics, Hindawi, vol. 2004, pages 1-16, January.
    3. Chen, Yuanyuan & Yu, Jiang & Sun, Chengjun, 2007. "Stability and Hopf bifurcation analysis in a three-level food chain system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 683-694.
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    Cited by:

    1. Hu, Guang-Ping & Li, Wan-Tong & Yan, Xiang-Ping, 2009. "Hopf bifurcations in a predator–prey system with multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1273-1285.
    2. Ling, Li & Wang, Weiming, 2009. "Dynamics of a Ivlev-type predator–prey system with constant rate harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2139-2153.
    3. Dhar, Joydip & Singh, Harkaran & Bhatti, Harbax Singh, 2015. "Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 324-335.

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