Study of Generalized Chaotic Synchronization Method Incorporating Error-Feedback Coefficients

In this paper, taking the generalized synchronization problem of discrete chaotic systems as a starting point, a generalized synchronization method incorporating error-feedback coefficients into the controller based on the generalized chaos synchronization theory and stability theorem for nonlinear systems is proposed. Two discrete chaotic systems with different dimensions are constructed in this paper, the dynamics of the proposed systems are analyzed, and finally, the phase diagrams, Lyapunov exponent diagrams, and bifurcation diagrams of these are shown and described. The experimental results show that the design of the adaptive generalized synchronization system is achievable in cases in which the error-feedback coefficient satisfies certain conditions. Finally, a chaotic hiding image encryption transmission system based on a generalized synchronization approach is proposed, in which an error-feedback coefficient is introduced into the controller.

Automated summary

In this paper, a generalized synchronization method incorporating error-feedback coefficients into the controller based on the generalized chaos synchronization theory and stability theorem for nonlinear systems is proposed. The dynamics of two constructed discrete chaotic systems are analyzed and their phase diagrams, Lyapunov exponent diagrams, and bifurcation diagrams are shown. Experimental results demonstrate the feasibility of the design of an adaptive generalized synchronization system under certain conditions of the error-feedback coefficient. Finally, a chaotic hiding image encryption transmission system based on a generalized synchronization approach is proposed, introducing an error-feedback coefficient into the controller.