一个含指数函数的混沌系统设计与电路实现

摘要

In order to enrich the types of chaotic systems, we propose a new chaotic system by using an exponential function instead of a nonlinear term in the Lorenz system, and analyze the basic dynamic characteristics of the system, such as the symmetry of the system, the stability of equilibrium point,the Lyapunov index and Lyapunov dimension, and so on. Compared with the Lorenz system, the balance point of the new system does not contain the origin,has a greater positive Lyapunov index,and can produce more complex chaotic attractor. An electronic circuit is designed to achieve the system, and the experimental results are in line with that of numerical simulations.%为丰富混沌系统类型,通过将Lorenz系统中的一个非线性项用指数函数替代的方法,获得一个新的混沌系统.分析了该系统的对称性、平衡点的稳定性、Lyapunov指数和Lyapunov维数等基本动力学特性.与Lorenz系统相比,新系统的平衡点不包含原点,且具有更大的正Lyapunov指数,能够产生更为复杂的混沌吸引子.设计的电子电路实现了该系统,电路实验结果与数值仿真一致.