On Coexistence of Fractional-order Hidden attractors

[+] Author and Article Information
Manashita Borah

Faculty, Department of Electrical Engineering, Tezpur University, Tezpur, 784028, India

1Corresponding author.

ASME doi:10.1115/1.4039841 History: Received August 01, 2017; Revised March 21, 2018


This paper proposes new fractional-order models of seven non-equilibrium or stable equilibrium systems and investigates the existence of chaos and hyperchaos in them. It thereby challenges the conventional generation of chaos that involves starting the orbits from the vicinity of unstable manifold. This is followed by the discovery of coexisting hidden attractors in fractional dynamics. All the seven newly proposed fractional-order chaotic systems (FOCSs) ranging from minimum fractional dimension (n_f) of 2.76 to 4.95, exhibit multiple hidden attractors, such as periodic orbits, stable foci, and strange attractors, often coexisting together. To the best of the author's knowledge, this phenomenon of prevalence of fractional-order (FO) coexisting hidden attractors in multidimensional FOCSs is reported for the first time. These findings have significant practical relevance because the attractors are discovered in real-life physical systems such as the FO homopolar disc dynamo, FO memristive system, FO model of the modulation instability in a dissipative medium, etc., as analysed in this work. Numerical simulation results confirm the theoretical analyses and comply with the fact that multistability of hidden attractors does exist in the proposed FO models.

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