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Dynamical analysis of a new three-dimensional fractional chaotic system

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Abstract

In the present paper, a new fractional chaotic system proposed by the authors is discussed. Moreover, based on the stability theory of fractional-order systems, conditions for the stability of nonlinear fractional-order systems are presented, and the existence and uniqueness of the solutions of the resulting new fractional chaotic attractor are also studied. Next, the necessary conditions for the existence of chaotic attractors in new fractional chaotic system are reported, and at the end the stability analysis of the corresponding equilibria is given. Last but not the least, the presented numerical simulations confirm the validity of our analysis.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran

    P Gholamin & A H Refahi Sheikhani

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  1. P Gholamin
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  2. A H Refahi Sheikhani
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Correspondence to A H Refahi Sheikhani.

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Gholamin, P., Sheikhani, A.H.R. Dynamical analysis of a new three-dimensional fractional chaotic system. Pramana - J Phys 92, 91 (2019). https://doi.org/10.1007/s12043-019-1738-y

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  • DOI: https://doi.org/10.1007/s12043-019-1738-y

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