To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincaré section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.
In this paper,a simplest fractional-order hyperchaotic(SFOH)system is obtained when the fractional calculus is applied to the piecewise-linear hyperchaotic system,which possesses seven terms without any quadratic or higher-order polynomials.The numerical solution of the SFOH system is investigated based on the Adomian decomposition method(ADM).The methods of segmentation and replacement function are proposed to solve this system and analyze the dynamics.Dynamics of this system are demonstrated by means of phase portraits,bifurcation diagrams,Lyapunov exponent spectrum(LEs)and Poincarésection.The results show that the system has a wide chaotic range with order change,and large Lyapunov exponent when the order is very small,which indicates that the system has a good application prospect.Besides,the parameter a is a partial amplitude controller for the SFOH system.Finally,the system is successfully implemented by digital signal processor(DSP).It lays a foundation for the application of the SFOH system.
