The Hopf bifurcation analysis in a delayed fractional SIR epidemic model

Pan, Feng; Cui, Xinshu; Xue, Dingyü; Liu, Lu

doi:10.1109/ccdc.2018.8407653

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“…A time delay may have a very complicated impact on the dynamical behaviour of the system such as the periodic structure, bifurcation and so forth. For references, see [4–9, 13, 14, 17, 22, 23, 27, 31–33]. There have been many works which are devoted to the studies of dynamical behaviours for predator-prey systems with various functional responses.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation Analysis of a Fractional-Order Holling–tanner Predator-Prey Model With Time Delay

Çelik

DEGERLİ

2022

ANZIAM J.

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We study a fractional-order delayed predator-prey model with Holling–Tanner-type functional response. Mainly, by choosing the delay time $\tau $ as the bifurcation parameter, we show that Hopf bifurcation can occur as the delay time $\tau $ passes some critical values. The local stability of a positive equilibrium and the existence of the Hopf bifurcations are established, and numerical simulations for justifying the theoretical analysis are also presented.

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