一类多涡卷混沌系统构造方法研究

提出一种基于平移变换的多涡卷混沌系统构造方法.首先选取合适的不稳定线性系统，利用一系列相互平行的分界面对相空间进行划分，然后通过对该线性系统进行平移变换，使新系统作用于相应的空间区域，最后利用基于符号函数的非线性函数来统一表示整个系统.根据该方法可以构造具有任意奇数个涡卷的新型混沌系统，同时也可以对某些现有混沌系统进行改进，使之成为多涡卷系统.数值仿真结果验证了该方法的可行性.关键词：多涡卷混沌吸引子平移变换涡卷

Studies on the construction method of a family of multi-scroll chaotic systems

A method for constructing multi-scroll chaotic systems based on shift transformation is presented. Firstly a proper unstable linear system is selected, and the phase space is divided into several parts by a series of parallel interfaces. Then shift transformations of the linear system are implemented so that each space region is dominated by the corresponding new system. Finally the whole system is obtained using a proper nonlinear function based on signum functions. According to this method new multi-scroll chaotic systems with arbitrary odd number scrolls can be constructed, furthermore, some existing chaotic systems can also be modified into multi-scroll systems. Numerical simulations verify the feasibility of the proposed method.