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Effect of fractional order on the stability and the localisation of the critical Hopf bifurcation value in a fractional chaotic system

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Abstract

In this paper, the stability of a fractional-order chaotic Jerk system is investigated, using the Routh–Hurwitz criteria. Hopf bifurcation analysis versus the fractional order and a parameter is done. Under the bifurcation parameter, some conditions ensuring the Hopf bifurcation, in the fractional order and its counterpart integer order, are proposed. Furthermore, numerical investigations are performed by taking commensurate and incommensurate fractional chaotic systems, it has been observed that under the influence of fractional order, the location of the critical Hopf bifurcation value changes, causing the system to exhibit reduced chaotic behaviour. Tables and some figures are given to illustrate and verify the results.

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  1. Besma Chettouh and Tidjani Menacer have contributed equally to this work.

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  1. Laboratory of Applied Mathematics, Mohamed Khider University, Biskra, Algeria

    Besma Chettouh & Tidjani Menacer

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  1. Besma Chettouh
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  2. Tidjani Menacer
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These authors contributed equally to this work.

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Correspondence to Tidjani Menacer.

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Chettouh, B., Menacer, T. Effect of fractional order on the stability and the localisation of the critical Hopf bifurcation value in a fractional chaotic system. Int. J. Dynam. Control (2023). https://doi.org/10.1007/s40435-023-01303-5

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  • DOI: https://doi.org/10.1007/s40435-023-01303-5

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