超混沌系统的构造方法研究

摘要

分析了Lorenz系统的结构，提出了基于Lorenz系统通过增加微分方程组维数和引入非线性项来构造超混沌系统要满足的必要条件和规则，并按照引入新变量增加微分方程组维数和增加非线性项的构造超混沌系统规则，分别构造了一个新的四维超混沌Lorenz系统和一个五维超混沌Lorenz系统，最后将所提出的两个新的超混沌Lorenz系统与其他混沌系统进行了对比分析，结果表明新的混沌系统具有良好的动力学特性，可提供更大的密钥空间，以及增强了动力学系统的非线性，为图像加密提供了新方法，同时也丰富了混沌学理论。%In this paper, by analyzing the Lorenz system’s structure, increasing the dimension of the differential equa-tions and introducing a nonlinear term, a necessary condition for hyperchaotic system is proposed based on the Lorenz sys-tem, according to which a new four-dimensional hyperchaotic Lorenz system and a five-dimensional hyperchaotic Lorenz system are constructed, respectively. The two new hyperchaotic systems are compared with other chaotic systems, and the results reveal that the new chaotic systems have good dynamic characteristics and can provide a larger key space and a bet-ter dynamic nonlinearity, which not only provides a new way for image encryption, but also enriches the chaos theory.