BIFURCATION BEHAVIORS OF A FRACTIONAL-ORDER PREDATOR–PREY NETWORK WITH TWO DELAYS

Chengdai Huang ()
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Chengdai Huang: School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

FRACTALS (fractals), 2021, vol. 29, issue 06, 1-17

Abstract: This paper highlights the stability and bifurcation of a fractional-order predator–prey model involving two delays. The critical values of delays with respect to Hopf bifurcation are exactly calculated for the developed model by taking two different delays as bifurcation parameters, respectively. Moreover, the effects of fractional order and additional delay on the bifurcation point are carefully explored. It detects that the stability performance is extremely strengthened by taking an appropriate fractional order and another delay. This hints that the onset of Hopf bifurcation can be advanced (lagged) with variations of their values. Numerical simulations are ultimately employed to check the correctness of the derived theoretical analysis.

Keywords: Double Delays; Stability; Hopf Bifurcation; Fractional-Order; Predator–Prey System (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X2150153X

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