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Hyper-chaotic analysis and adaptive multi-switching synchronization of a novel asymmetric non-linear dynamical system

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Abstract

In this paper, a new 4D autonomous asymmetric hyperchaotic system obtained from a three dimensional autonomous chaotic system is introduced. We analyse the hyperchaotic properties of the new system such as dissipation, equilibrium, Lyapunov exponent, stability, time series, phase portraits, Poincare map and bifurcation diagram. Furthermore, the multi-switching synchronization of the new asymmetric hyperchaotic system is analysed by using the adaptive control strategy. Based on the theory of Lyapunov stability, we sketch the input controllers and updating laws of distinct switching, and it is extended to examine the synchronization problems of response and drive systems with distinct combinations. Brief theoretical analysis and numerical results are presented to show the dynamical behaviour of the new 4D hyperchaotic system.

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Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, New Delhi, 110025, India

    Ayub Khan & Muzaffar Ahmad Bhat

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  1. Ayub Khan
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  2. Muzaffar Ahmad Bhat
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Correspondence to Muzaffar Ahmad Bhat.

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Khan, A., Bhat, M.A. Hyper-chaotic analysis and adaptive multi-switching synchronization of a novel asymmetric non-linear dynamical system. Int. J. Dynam. Control 5, 1211–1221 (2017). https://doi.org/10.1007/s40435-016-0274-6

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  • DOI: https://doi.org/10.1007/s40435-016-0274-6

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