Analysis Of A Novel Chaotic System And Its Synchronization

Chaos, as one of the important parts of nonlinear science, reveals the complex of the natural world and human society, and it is the unity of order and disorder and the unity of certainty and randomness. People’s vision is broaden and the understanding of the objective world is deepen. In recent years, the study of chaos control and synchronization becomes the basis of the current natural science and one of the most popular topics.A new chaotic system is presented in this paper. The complicated dynamic behaviors are studied when the parameters are given, and the oscillator circuit of the system is designed. The chaotic characteristics of the new system are verified through theoretical analysis and numerical simulations. It has good chaotic features, such as the larger Lyapunov exponent, continuous broadband spectrum, sensitive dependence on initial values and so on. In addition, the design methods of synchronization of the new chaotic system is analyzed. First, the synchronization and anti-synchronization of the chaotic systems is achieved using nonlinear feedback method. Secondly, the synchronization of the chaotic systems can be realized rapidly by solving the state feedback matrix to design a state observer. This method does not need to construct Lyapunov functions, or calculate the Lyapunov condition exponents. Finally, the chaos synchronization based on nonlinear coupling method is introduced, and the complex network synchronizations, including the full connectivity network synchronization and star network synchronization, are analyzed respectively. Simulation results validate the effectiveness and feasibility of the design methods, which have good application prospects.