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HOPF BIFURCATION ANALYSIS OF A FRACTIONAL-ORDER HOLLING–TANNER PREDATOR-PREY MODEL WITH TIME DELAY

Part of: General theory in ordinary differential equations Functional-differential and differential-difference equations

Published online by Cambridge University Press:  05 April 2022

C. CELIK Open the ORCID record for C. CELIK [Opens in a new window]  and
K. DEGERLİ Open the ORCID record for K. DEGERLİ [Opens in a new window]
C. CELIK*
Affiliation:
Faculty of Arts and Sciences, Department of Mathematics, Yildiz Technical University, İstanbul, Turkey
K. DEGERLİ
Affiliation:
Faculty of Engineering and Natural Sciences, Department of Mathematics, Bahcesehir University, İstanbul, Turkey; e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

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.

Keywords

fractional-ordertime-delayHopf bifurcationpredator-prey system

MSC classification

Primary: 34A08: Fractional differential equations
Secondary: 34K18: Bifurcation theory 34K20: Stability theory
Type
Research Article
Information
The ANZIAM Journal , Volume 64 , Issue 1 , January 2022 , pp. 23 - 39
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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