一类延迟混沌系统沿主轴方向上Lyapunov指数的计算方法

提出了一种计算延迟混沌系统沿主轴方向上Lyapunov指数的方法：矩阵迭代法.给出了其计算方法的原理及推导过程；同时推导了一类泰勒展开法，介绍了已有的Wolf替代法计算延迟混沌系统的Lyapunov指数.分析了三种不同计算方法的优缺点，最后进行了数值模拟，验证方法的有效性. 关键词： Lyapunov指数 延迟混沌系统 矩阵迭代法 泰勒展开法

Methods for calculating the main-axis Lyapunov exponents of a type of chaotic systems with delay

In this paper，we propose a new method for calculating the main-axis Lyapunov exponents of a type of chaotic systems with delays，which we call Matrix iteration method. We discuss this new method theoretically by detailed analysis. Also，we introduce another method called Taylor expansion method. The method invented by Wolf is also introduced and we discuss the advantages and disadvantages of these three methods. Finally，we calculate the main-axis Lyapunov exponents of a type of chaotic systems with delay to test these method.