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Dynamical Analysis of a Delayed Reaction-Diffusion Predator-Prey System

Author

Listed:
  • Yanuo Zhu
  • Yongli Cai
  • Shuling Yan
  • Weiming Wang

Abstract

This work deals with the analysis of a delayed diffusive predator-prey system under Neumann boundary conditions. The dynamics are investigated in terms of the stability of the nonnegative equilibria and the existence of Hopf bifurcation by analyzing the characteristic equations. The direction of Hopf bifurcation and the stability of bifurcating periodic solution are also discussed by employing the normal form theory and the center manifold reduction. Furthermore, we prove that the positive equilibrium is asymptotically stable when the delay is less than a certain critical value and unstable when the delay is greater than the critical value.

Suggested Citation

  • Yanuo Zhu & Yongli Cai & Shuling Yan & Weiming Wang, 2012. "Dynamical Analysis of a Delayed Reaction-Diffusion Predator-Prey System," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-23, October.
    • Handle: RePEc:hin:jnlaaa:323186
    DOI: 10.1155/2012/323186
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    Cited by:

    1. Xinhong Pan & Min Zhao & Chuanjun Dai & Yapei Wang, 2014. "Stability and Hopf Bifurcation Analysis of a Nutrient‐Phytoplankton Model with Delay Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Weifang Yan & Rui Liu, 2013. "Existence and Asymptotic Behavior of Traveling Wave Fronts for a Time‐Delayed Degenerate Diffusion Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Xinhong Pan & Min Zhao & Yapei Wang & Hengguo Yu & Zengling Ma & Qi Wang, 2014. "Stability and Dynamical Analysis of a Biological System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Xinze Lian & Guichen Lu & Hailing Wang, 2014. "Pattern Formation in a Bacterial Colony Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Xinhong Pan & Min Zhao & Chuanjun Dai & Yapei Wang, 2015. "Dynamic Analysis of a Delayed Reaction‐Diffusion Predator‐Prey System with Modified Holling‐Tanner Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

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