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Lyapunov exponents; bifurcation diagram; Poincare section map and satellite systems

In this paper, we analyse the chaotic satellite system using dissipativity, equilibrium points, bifurcation diagrams, Poincare section maps, Lyapunov exponents and Kaplan–Yorke dimension. We obtain the equilibrium points of chaotic satellite system and at each equilibrium point, we obtain the eigenvalue of Jacobian matrix of the satellite system to verify the unstable region.We calculate the Kaplan–Yorke dimension, which ensures the strange behaviour of the system. We observe closely the three-dimensional (3D) phase portraits of the satellite system at different parameter values. We plot the Lyapunov exponent graphs corresponding to every 3D phase portrait of satellite systems, to verify the chaoticity of satellite systems. We establish time-delay synchronisation for twoidentical satellite systems. The simulated and qualitative results are in an excellent agreement.

AYUB KHAN¹ SANJAY KUMAR¹

1. Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110 025, India

Published

1 October 2018

Manuscript received

18 November 2017

Manuscript revised

31 January 2018

Accepted

1 February 2018

Early published

Unedited version published online

Final version published online

11 August 2018