, 91:49 | Cite as

Analysis and time-delay synchronisation of chaotic satellite systems

  • Ayub Khan
  • Sanjay KumarEmail author


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 two identical satellite systems. The simulated and qualitative results are in an excellent agreement.


Lyapunov exponents bifurcation diagram Poincare section map and satellite systems 


05.45.Tp 05.45.Vx 05.45.Gg 05.45.Pq 


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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Natural SciencesJamia Millia IslamiaNew DelhiIndia

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