Time-delay Synchronization Of Different-Lags Chaotic Systems And Its Circuit Simulation

The dynamic behaviors of delay chaotic systems are not only with continuous time, but also with the front of the period t closely associated. Time lag systems are often encountered in daily life and works, especially delays and random perturbation problems are important factors affecting the stability and control of the quality control systems. This article is mainly for construction, analysis, simulation and synchronization control of chaotic system,from non-delay to different delays, from the integer order chaotic system delay synchronization to fractional chaotic system delay synchronization, gradually, step by step for analysis and research, focused on research contents are as follows:(1) Four models of chaotic systems are constructed. The theoretical analysis and numerical simulation prove chaotic behavior and circuit simulation shows the chaotic systems can be implemented on the physical.(2) 4 kinds of circuit unit forms are introduced, namely fractional chain type, tree type,mixed type and new type. Based on them, simulations of the combinational circuits with different fractional order are made. A heterogeneity circuit(circuit unit different from each other) is selected from fractional order q which values all the same, not all the same and all different, to make analysis and simulations. The experiment results prove effectiveness and flexibility of the multiple circuit design and also demonstrate that the fractional-order chaotic system can be implemented on the physical.(3) It constructs the corresponding delay chaotic system model by introducing delay parameters, and the basic dynamic analysis and circuit simulation results show that the time-delay chaotic system models can be implemented on the physical.(4) Respectively it studied on delayed feedback control and drive-response delay control of the different-lags chaotic systems, the theory verified the effectiveness of the controller design. For a class of parameter uncertainty fractional different-lags chaotic systems, it designs a time-delayed synchronization controllers and parameter adaptive laws. It proves that the drive system and the response system tend to be synchronized and identified parameter when the control parameter matrix K satisfies the condition that K -n E is a positive definite matrix. Simulation results show physical realizability of the fractional-order different-lags chaotic system and verify effectiveness of different-lags synchronization in time-delayedsystem method design.Due to the time delay introduced, it can enhance the pseudorandom sequence and long-term unpredictability in the nonlinear dynamical systems. Theoretical analysis and circuit simulation results are illustrated that the time-delay chaotic system models can be implemented on the physical and the effectiveness of delay synchronization control design.Research results achieved provides a certain reference value of chaos theory in practical applications.