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Bifurcations in a predator-prey model with discrete and distributed time delay

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Abstract

In this paper, a class of predator-prey model with discrete and distributed time delay is considered. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By using the normal form theory and center manifold theory, we derive some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are included.

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Authors and Affiliations

  1. Guizhou Key Laboratory of Economics System Simulation, Guizhou College of Finance and Economics, Guiyang, 550004, P.R. China

    Changjin Xu

  2. Department of Mathematics and Physics, Guilin University of Technology, Guilin, Guangxi, 541004, P.R. China

    Yuanfu Shao

Authors
  1. Changjin Xu
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  2. Yuanfu Shao
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Corresponding author

Correspondence to Changjin Xu.

Additional information

This work is supported by Doctoral Foundation of Guizhou College of Finance and Economics (2010) and Scientific Research Fund of Hunan Provincial Education Department (No. 10C0560).

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Xu, C., Shao, Y. Bifurcations in a predator-prey model with discrete and distributed time delay. Nonlinear Dyn 67, 2207–2223 (2012). https://doi.org/10.1007/s11071-011-0140-1

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  • DOI: https://doi.org/10.1007/s11071-011-0140-1

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