最大 Lyapunov 指数在确定混沌系统混沌参数域中的应用

摘要

Nonlinear vibration systems have some characteristics and properties different from traditional linear vibration systems.When the pa-rameter is in some ranges,the system is in a chaot-ic state.The largest Lyapunov exponent is an es-sential criterion to judge whether the system is in chaos state or not.The feasibility of using the Lar-gest Lyapunov exponent to confirm the parameter domain is presented in this paper,and it is verified by the bifurcation diagram of system.%非线性振动系统具有与传统线性振动系统不同的某些特点和性能，并且当参数处于一定范围内时，系统将呈现混沌状态。最大 Lyapunov 指数是判断非线性振动系统是否为混沌的一个重要判据。提出了利用最大 Lyapunov 指数来确定 Duf-fing 系统的混沌参数区间的可行性，并利用参数的分岔图进行验证。