DYNAMICS OF FRACTIONAL-ORDER PREDATOR–PREY MODEL INCORPORATING TWO DELAYS

Lingzhi Zhao (), Chengdai Huang and Jinde Cao
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Lingzhi Zhao: School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, P. R. China
Chengdai Huang: School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China
Jinde Cao: School of Mathematics, Southeast University, Nanjing 210096, P. R. China4Yonsei Frontier Lab, Yonsei University, Eeoul 03722, South Korea

FRACTALS (fractals), 2021, vol. 29, issue 01, 1-14

Abstract: This paper studies the problem of bifurcation for a fractional-order predator–prey system with two different delays by considering fractional interval (0, 2]. Multiple delays-depended stability domains of the developed model are procured and the bifurcation points are exactly established by taking advantage of two different delays as bifurcation parameters, respectively. It detects that the stability performance can be extremely varied with the changes of control parameter upon one delay is established. System possesses excellent stability performance when choosing the smaller control parameter, and Hopf bifurcation emerges from system once control parameter passes through the critical values, which degrades the performance of the system. Numerical simulations are finally performed to check our theoretical analysis.

Keywords: Fractional Order; Different Delays; Stability; Hopf Bifurcation; Predator–Prey System (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500146

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