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Hopf bifurcation in a predator–prey system with discrete and distributed delays

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  • Yang, Yu
  • Ye, Jin

Abstract

In this paper, a predator–prey system with discrete and distributed delays is considered. By regarding the delay as the bifurcation parameter and analyzing the associated characteristic equation of the original system at the positive equilibrium, it is found that Hopf bifurcations occur when the delay passes through a certain critical value. Finally, numerical simulations are given to support our theoretical results.

Suggested Citation

  • Yang, Yu & Ye, Jin, 2009. "Hopf bifurcation in a predator–prey system with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 554-559.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:554-559
    DOI: 10.1016/j.chaos.2009.01.026
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    References listed on IDEAS

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    1. Li, Xiuling & Wei, Junjie, 2005. "On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 519-526.
    2. Zheng, Baodong & Zhang, Yazhuo & Zhang, Chunrui, 2008. "Global existence of periodic solutions on a simplified BAM neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1397-1408.
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    Cited by:

    1. Tang, Xiaosong, 2022. "Periodic solutions and spatial patterns induced by mixed delays in a diffusive spruce budworm model with Holling II predation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 420-429.

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