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Switching synchronisation control between integer-order and fractional-order dynamics of a chaotic system

This paper aims at enhancing the level of security in chaotic communication for which a switching synchronisation scheme is designed. The authors propose a novel fractional-order chaotic system (FOCS) which undergoes switching between integer-order and fractional-order dynamical subsystems with the help of the synchronisation scheme put forward. The new fractional-order model displays rich bifurcations undergoing two period doubling routes to chaos, where the fractional order α is the bifurcation parameter. Study of the strange attractor dynamics is carried out with the aid of phase portraits, sensitivity to initial conditions, fractal Lyapunov dimension, maximum Lyapunov exponents spectrum and bifurcation analysis. The minimum commensurate dimension to display chaos is determined. Finally the theoretical analyses are validated by numerical simulation results which are in good agreement with each other. With a view to utilizing it in enhancing the safety performance of secure communication, chaos based cryptology and coding information, the authors are hopeful that this switching control scheme will aid in bridging the gap between integer and fractional-order synchronisation.