关键词: 超混沌系统, Lorenz系统, Lyapunov指数, 图像加密

Abstract: In this paper, by analyzing the Lorenz system’s structure, increasing the dimension of the differential equations and introducing a nonlinear term, a necessary condition for hyperchaotic system is proposed based on the Lorenz system, 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 better dynamic nonlinearity, which not only provides a new way for image encryption, but also enriches the chaos theory.

Key words: hyperchaotic system, Lorenz system, Lyapunov exponents, image encryption