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Computations of synchronisation conditions in some fractional-order chaotic and hyperchaotic systems

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Abstract

A novel criterion for achieving synchronisation in fractional-order chaotic and hyperchaotic systems is presented. Here, it is proved that the existence of a Lyapunov function in the integer-order differential system implies local stability of the steady state in its fractional-order counterpart. So, our criterion is based on computations of suitable linear feedback controllers of the fractional-order systems according to an appropriate choice of Lyapunov function. Furthermore, a new fractional-order hyperchaotic system is introduced here. The case of hyperchaos in the proposed system is verified by computing its greatest two Lyapunov exponents which are shown to be positive. The new synchronisation criterion is successfully applied to the fractional Liu system, the fractional Samardzija–Greller system, the fractional financial system and a novel fractional-order hyperchaotic system. Numerical results are used to verify the analytical results.

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Acknowledgements

This work is supported by the Deanship of Scientific Research at King Saud University, Research Group No. RG-1438-046. The authors appreciate the valuable comments given by the anonymous reviewers that help to improve the presentation of our work.

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Al-Khedhairi, A., Matouk, A.E. & Askar, S.S. Computations of synchronisation conditions in some fractional-order chaotic and hyperchaotic systems. Pramana - J Phys 92, 72 (2019). https://doi.org/10.1007/s12043-019-1747-x

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  • DOI: https://doi.org/10.1007/s12043-019-1747-x

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