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A novel strategy of bifurcation control for a delayed fractional predator–prey model

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  • Huang, Chengdai
  • Li, Huan
  • Cao, Jinde

Abstract

This paper aims at controlling bifurcation of a fractional predator–prey system by an original extended delayed feedback controller. Firstly, some sufficient conditions of delay-induced bifurcations for such uncontrolled system are captured regarding time delay as a bifurcation parameter. Secondly, a generalised delayed feedback controller is subtly designed to control Hopf bifurcation for the proposed system. It suggests that bifurcation dynamics can be controlled efficaciously for such system by carefully adjusting extended feedback delay or fractional order so long as the other parameters are established. Thirdly, the bifurcation diagrams are meticulously plotted. The obtained results consumedly popularize the previous studies concerning bifurcation control of delayed fractional-order systems. To underline the effectiveness of the proposed control scheme, some numerical simulations are ultimately addressed.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:808-838
    DOI: 10.1016/j.amc.2018.11.031
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    Cited by:

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    5. 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.
    6. Ghosh, Uttam & Pal, Swadesh & Banerjee, Malay, 2021. "Memory effect on Bazykin’s prey-predator model: Stability and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    7. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Cao, Jinde & Alsaedi, Ahmed, 2020. "Extended feedback and simulation strategies for a delayed fractional-order control system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    8. Kaviya, R. & Priyanka, M. & Muthukumar, P., 2022. "Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    9. Ghanbari, Behzad & Djilali, Salih, 2020. "Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    10. Li, Peiluan & Gao, Rong & Xu, Changjin & Li, Ying & Akgül, Ali & Baleanu, Dumitru, 2023. "Dynamics exploration for a fractional-order delayed zooplankton–phytoplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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