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Dynamical Analysis of a Prabhakar Fractional Chaotic Autonomous System

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Nonlinear Dynamics and Complexity

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 36))

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Abstract

In this chapter, we introduce a new chaotic autonomous system with the fractional regularized Prabhakar derivative. Then, we prove the existence and uniqueness of the solution to the mentioned system. We also give a numerical scheme for the system and state a theorem to analyze the stability of the system based on the Lyapunov second method. Next, we eliminate the chaotic behaviors of the system by means of a feedback controller and presented theorem. Moreover, synchronization is achieved between two regularized Prabhakar fractional chaotic autonomous systems. We further present numerical simulations and reveal asymptotic stability and chaotic behaviors of the system to verify the theoretical analysis. Furthermore, we show that the parameters of the fractional regularized Prabhakar derivative play the important role in the dynamic behaviors of the system and the chaotic behavior reduces and even eliminates by choosing the appropriate parameters of the fractional regularized Prabhakar derivative in the system.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

    Shiva Eshaghi & Yadollah Ordokhani

Authors
  1. Shiva Eshaghi
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  2. Yadollah Ordokhani
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Correspondence to Shiva Eshaghi .

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Editors and Affiliations

  1. School of Engineering, Polytechnic Institute of Porto, Porto, Portugal

    Carla M.A. Pinto

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Eshaghi, S., Ordokhani, Y. (2022). Dynamical Analysis of a Prabhakar Fractional Chaotic Autonomous System. In: Pinto, C.M. (eds) Nonlinear Dynamics and Complexity. Nonlinear Systems and Complexity, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-031-06632-0_19

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