A financial hyperchaotic system with coexisting attractors : dynamic investigation, entropy analysis, control and synchronization

Abstract

This paper is concerned with dynamic and entropy analyses of a hyperchaotic financial system, as well as with its hyperchaos suppression and synchronization. The dynamic behaviour of the system is analyzed for several parameters and initial conditions making use of bifurcation diagrams, Lyapunov exponents and phase portraits. Moreover, entropy from resulting time series is also characterized by estimating ordinal pattern distributions. These analyses have been able to determine and locate accurately chaotic and periodic attractors in the system, thus enabling successful design of its control. In general, financial systems are not always completely synchronized; therefore, some robust synchronization technique should be considered. This study proposes a novel fuzzy disturbance-observer based integral terminal sliding mode control method for the hyperchaotic financial system. The presented control technique guarantees robustness against uncertainties, external disturbances and control input saturation. Fuzzy rules are employed to adaptively tune the gains of the proposed control scheme. Also, the fuzzy inference engine avoids the chattering problem in the system response. Simulation results illustrate the efficient performance of the proposed control technique in presence of dynamic uncertainties, external disturbances and control input saturation.