Abstract: A novel three-dimensional chaotic system is constructed. The dynamic properties of the new system are investigated and it also shows that there exists chaotic behavior and chaotic attractor, and the circuit simulation results show physical realizability of the chaotic system. It designs a new different-lags chaotic system. Numerical analysis and circuit simulation results show physical realizability of the different-lags chaotic system. For a class of parameters uncertainty 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, when the control parameter matrix [K] satisfies the condition that [K-nE] is a positive definite matrix. Numerical simulation results show effectiveness of different-lags synchronization in time-delayed system method design.

Key words: different-lags chaotic system, parameters uncertainty, adaptive lag synchronization control, circuit simulation

摘要： 构建一个新三维混沌系统，通过对系统非线性动力学特性进行分析，证实了系统的混沌特性并确定其混沌吸引子的存在，电路仿真说明了该混沌系统的物理可实现性。设计了该混沌系统的异时滞混沌系统，数值分析和电路仿真表明了异时滞混沌系统的物理可实现性。对一类参数不确定的时滞混沌系统的自适应延时同步进行讨论，以Lyapunov-Krasovskii泛函为理论基础，设计了时滞延时同步控制器，从理论上证明了当控制参数矩阵[K]满足[K-nE]为正定矩阵时，驱动系统与响应系统趋于同步，数值仿真表明了异时滞延时同步方法设计的普适性和有效性。

关键词: 异时滞混沌系统, 不确定参数, 自适应延时同步控制, 电路仿真