Anti-control And Circuit Implementation Research Of Lorenz Family Chaotic Systems

Abstract:Chaos anti-control is a hot topic in the current field of chaos control. With theoretical analysis, numerical simulation and circuit experiment, switching control, feedback control and coupling control based on the family of Lorenz chaotic system have been studied. More complex systems have been obtained. The results have theoretical significance and practical value.By changing some control coefficients in the unified chaotic system, three simplified models with different topology were proposed. Basic properties and dynamical behaviors were analyzed with numerical simulations. And the three systems were integrated in a common circuit and easily switched by a DIP switch.A linear feedback and a nonlinear feedback were added to the simplified Lorenz system. Then a five-dimensional chaotic system was produced. By fixing the parameters, the Lyapunov exponents and bifurcation were analyzed with diffferent parameters. When the parameters are in some ranges, the system has three positive Lyapunov exponents, that is, it has a higher system complexity.A six-dimensional nonlinear system was constructed by uni-directionally coupling two identical simplified Lorenz chaotic systems. Basic properties were analyzed. The dynamical evolution of the coupled system with variations of system parameter and coupling coefficients was investigated.The relationship between the dynamical behavior and synchronization was summarized. Circuit simulations were carried on the Multisim platform, the results had good agreement with the numerical simulation.Based on the switched unified chaotic systems, a chaos shift keying scheme for digital communication was designed. Based on the simplified Lorenz chaotic system, a chaos masking scheme for secure communication with coupled synchronization was built. With Lyapunov stability theory, a tracking control scheme based on the simplified Lorenz simplified Lorenz system could track any reference signal and it was proved theoretically that this control scheme is exponential convergence.