Characteristic Analysis And Synchronization Control Of Fractional-order Hyperchaotic Systems

Abstract:Characteristics of Fractional-order hyperchaotic systems and its control becomes a hot topic in the field of chaos theory and application. In this paper, taking the fractional-order simplified Lorenz hyperchaotic system as the model, adopting the theoretical analysis and numerical simulation method, the dynamical characteristics and synchronization control of the fractional-order simplified Lorenz hyperchaotic system are investigated. The results have theoretical significance and application value.By using the Adams-Bashforth-Moulton algorithm and MATLAB simulation platform, two fractional-order simplified Lorenz hyperchaotic systems, which are respectively designed by the feedback control and sinusoidal perturbation, are studied by means of the phase diagrams, bifurcation diagrams, the maximum Lyapunov exponents, and Poincare section and so on. The dynamical behaviors of the fractional-order chaotic systems are observed in detail with the system parameters and the fractional orders variation. The ranges of the parameters in which the system generates chaos are determined. The routes to chaos are presented by bifurcation diagrams, such as the period-doubling bifurcation, pitchfork bifurcation, etc. The results show that the fractional-order simplified Lorenz hyperchaotic system has abundant dynamical behaviors.Based on the stability theory of the fractional-order linear system, the synchronization between the fractional-order simplified Lorenz hyperchaotic systems are investigated by employing the active control and the coupling control strategy. The synchronizations are realized between the same two fractional-order hyperchaotic systems or the different fractional-order hyperchaotic systems with different initial values respectively. The simulations verified the effectiveness of the two synchronization control schemes. According the index of the synchronization set-up time and synchronization precision, the performances of the synchronization systems are analyzed. By simulations, we found the law that the synchronization set-up time decreases with the increasing of fractional order. It lays the theory and technology foundation for the application researches of the fractional-order hyperchaotic systems.