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Stability and bifurcation analysis of a fractional predator–prey model involving two nonidentical delays

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  • Yuan, Jun
  • Zhao, Lingzhi
  • Huang, Chengdai
  • Xiao, Min

Abstract

In this paper, the subject of bifurcation for a fractional order predator–prey system involving two nonidentical delays is nicely discussed. The critical values of delays for Hopf bifurcation are exactly calculated for the proposed model by using two nonidentical delays as bifurcation parameter, respectively. In addition, the effects of fractional order and additional delay on the bifurcation point are delicately explored. It detects that the stability performance is extremely pulverized with the enhancement of fractional order and another delay. This hints that the generation of Hopf bifurcation can be advanced as fractional order and another delay increase. The final numerical simulations gauge the correctness of the developed theoretical analysis.

Suggested Citation

  • Yuan, Jun & Zhao, Lingzhi & Huang, Chengdai & Xiao, Min, 2021. "Stability and bifurcation analysis of a fractional predator–prey model involving two nonidentical delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 562-580.
    • Handle: RePEc:eee:matcom:v:181:y:2021:i:c:p:562-580
    DOI: 10.1016/j.matcom.2020.10.013
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    References listed on IDEAS

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    1. Yuan, Jun & Zhao, Lingzhi & Huang, Chengdai & Xiao, Min, 2019. "Novel results on bifurcation for a fractional-order complex-valued neural network with leakage delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 868-883.
    2. Li, Li & Wang, Zhen & Li, Yuxia & Shen, Hao & Lu, Junwei, 2018. "Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 152-169.
    3. Guin, Lakshmi Narayan & Baek, Hunki, 2018. "Comparative analysis between prey-dependent and ratio-dependent predator–prey systems relating to patterning phenomenon," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 100-117.
    4. Huang, Chengdai & Li, Huan & Cao, Jinde, 2019. "A novel strategy of bifurcation control for a delayed fractional predator–prey model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 808-838.
    5. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "Controlling bifurcation in a delayed fractional predator–prey system with incommensurate orders," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 293-310.
    6. Li, Huan & Huang, Chengdai & Li, Tongxing, 2019. "Dynamic complexity of a fractional-order predator–prey system with double delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
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    1. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.

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