Solution and dynamics of a fractional-order 5-D hyperchaotic system with four wings

Abstract

Based on the Adomian decomposition method (ADM), the numerical solution of a fractional-order 5-D hyperchaotic system with four wings is investigated. Dynamics of the system are analyzed by means of phase diagram, bifurcation diagram, Lyapunov exponents spectrum and chaos diagram. The method of one-dimensional linear path through the multidimensional parameter space is proposed to observe the evolution law of the system dynamics with parameters varying. The results illustrate that the system has abundant dynamical behaviors. Both the system order and parameters can be taken as bifurcation parameters. The phenomenon of multiple attractors is found, which means that some attractors are generated simultaneously from different initial values. The spectral entropy (SE) algorithm is applied to estimate the fractional-order system complexity, and we found that the complexity decreases with the increasing of system order. In order to verify the reliability of numerical solution, the fractional-order 5-D system with four wings is implemented on a DSP platform. The phase portraits of fractional-order system generated on DSP agree well with those obtained by computer simulations. It is shown that the fractional-order hyperchaotic system is a potential model for application in the field of chaotic secure communication.