一个新的混沌系统及其广义投影同步方法的研究

New chaotic system and its generalized projected synchronization method

利用标准的线性符号函数替换了Lorenz-Stenflo(LS)混沌系统的一个非线性项,重构得到了一个新的四维混沌系统,命名为修正的Lorenz-Stenflo(MLS)混沌系统.简化的结构使得该系统易于用电子线路实现.接着根据线性系统稳定性理论,结合非线性反馈控制方法,提出了MLS系统的广义投影同步方法.理论推导得到了2个MLS混沌系统实现广义投影同步的稳定条件.改进的投影同步控制器具有多个可变参数,可以自由设定系统的同步速度和同步形式.该方法适用范围广,应用灵活,简单易于实现.仿真结果验证了同步控制器可在多种同步形式下实现2个MLS混沌系统的广义同步,动态过程误差小.

A new four-dimensional system is constructed in this paper by replacing one of quadratic nonlinear terms of Lorenz-Stenflo （LS） system with a standard linear signal function. The new system is named modified Lorenz-Stenflo （MLS） system. The simple structure makes it easy to be realized in electronic circuits. Then using stability theory of linear systems and nonlinear feedback control, the generalized projected synchronization method of MLS systems is proposed in this paper. The stability conditions are analyzed for generalized projected synchronizing two MLS chaotic systems. There are changeable parameters within improved projected synchronization controllers, so that synchronization speed and formats can be freely set up. This method can be widely, agilely used and simply implemented. Simulation results show that synchronization controllers can generally synchronize two MLS chaotic systems in several different synchronization formats, meanwhile the dynamic process has small error values.