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Measure of chaos and adaptive synchronization of chaotic satellite systems

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Abstract

In this paper, we analyze the chaotic behaviour of satellite system through the dissipative, equilibrium points, bifurcation diagrams, Poincare section maps, Lyapunov exponents and Kaplan–Yorke dimension. We observe the qualitative behaviour of satellite systems through these tools to justify the chaos in the system. We obtain the equilibrium points of chaotic satellite system. At each equilibrium point we yield the eigenvalue of Jacobian matrix of satellite system and verify the unstable regions. We calculate Kaplan–Yorke dimension, \(D_{KY}= 2.1905\). Adaptive synchronization for two identical satellite systems is presented. The qualitative and simulated results are provided for verification of systems.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Natural Sciences, Jammia Millia Islamia, New Delhi, 110025, India

    Ayub Khan & Sanjay Kumar

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  1. Ayub Khan
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  2. Sanjay Kumar
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Correspondence to Sanjay Kumar.

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Khan, A., Kumar, S. Measure of chaos and adaptive synchronization of chaotic satellite systems. Int. J. Dynam. Control 7, 536–546 (2019). https://doi.org/10.1007/s40435-018-0481-4

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  • DOI: https://doi.org/10.1007/s40435-018-0481-4

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