Hidden attractor dynamics of a novel non-equilibrium fractional-order chaotic system and its synchronisation control

摘要

This paper presents a new fractional-order hidden strange attractor generated by a chaotic system without equilibria. The proposed non-equilibrium fractional-order chaotic system (FOCS) is asymmetric, dissimilar, topologically inequivalent to typical chaotic systems and challenges the conventional notion that the presence of unstable equilibria is mandatory to ensure the existence of chaos. The new fractional-order model displays rich bifurcation undergoing a period doubling route to chaos, where the fractional order α is the bifurcation parameter. Study of the hidden 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. With a view to utilizing it in chaos based cryptology and coding information, a synchronisation control scheme is designed. Finally the theoretical analyses are validated by numerical simulation results which are in good agreement with the former.