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The nature of Lyapunov exponents is (+, +, −, −). Is it a hyperchaotic system?

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  • Singh, Jay Prakash
  • Roy, B.K.

Abstract

This review paper aims at answering a basic question on the sign of Lyapunov exponents. A few recent papers reported hyperchaotic system having the sign of Lyapunov exponents as (+, +, −, −). Such (+, +, −, −) sign of Lyapunov exponents is in contradiction with the well known (+, +, 0, −) sign of Lyapunov exponents for a 4-D hyperchaotic system. This paper thus discusses various issues related to Lyapunov exponents and proves that the reported sign of (+, +, −, −) Lyapunov exponents is actually (+, +, 0, −) or (+, 0, −, −). This clarification is very important and essential since Lyapunov exponents are the only quantitative measure for the existence of hyperchaos. Three different algorithms are used for calculating the Laypunov exponents to prove the actual sign of Lyapunov exponents for a hyperchaotic system.

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  • Singh, Jay Prakash & Roy, B.K., 2016. "The nature of Lyapunov exponents is (+, +, −, −). Is it a hyperchaotic system?," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 73-85.
    • Handle: RePEc:eee:chsofr:v:92:y:2016:i:c:p:73-85
    DOI: 10.1016/j.chaos.2016.09.010
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    References listed on IDEAS

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    Cited by:

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    9. Singh, Jay Prakash & Roy, Binoy Krishna & Jafari, Sajad, 2018. "New family of 4-D hyperchaotic and chaotic systems with quadric surfaces of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 243-257.
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    11. Yadav, Vijay K. & Shukla, Vijay K. & Das, Subir, 2019. "Difference synchronization among three chaotic systems with exponential term and its chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 36-51.
    12. Maximenko, Vladimir A. & Hramov, Alexander E. & Koronovskii, Alexey A. & Makarov, Vladimir V. & Postnov, Dmitry E. & Balanov, Alexander G., 2017. "Lyapunov analysis of the spatially discrete-continuous system dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 228-237.
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