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Stability and bifurcation of a delayed generalized fractional-order prey–predator model with interspecific competition

Author

Listed:
  • Wang, Zhen
  • Xie, Yingkang
  • Lu, Junwei
  • Li, Yuxia

Abstract

The present paper considers a delayed generalized fractional-order prey-predator model with interspecific competition. The existence of the nontrivial positive equilibrium is discussed, and some sufficient conditions for global asymptotic stability of the equilibrium are developed. Meanwhile, the existence of Hopf bifurcation is discussed by choosing time delay as the bifurcation parameter. Finally, some numerical simulations are carried out to support the analytical results.

Suggested Citation

  • Wang, Zhen & Xie, Yingkang & Lu, Junwei & Li, Yuxia, 2019. "Stability and bifurcation of a delayed generalized fractional-order prey–predator model with interspecific competition," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 360-369.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:360-369
    DOI: 10.1016/j.amc.2018.11.016
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    References listed on IDEAS

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    1. Gan, Qintao & Xu, Rui & Yang, Pinghua, 2009. "Bifurcation and chaos in a ratio-dependent predator–prey system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1883-1895.
    2. Čermák, Jan & Došlá, Zuzana & Kisela, Tomáš, 2017. "Fractional differential equations with a constant delay: Stability and asymptotics of solutions," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 336-350.
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