基于QR分解的Duffing系统Lyapunov指数求解方法

QR Decomposition Based Method for the Computation of Lyapunov Exponent in Duffing Systems

Lyapunov指数衡量了非线性轨迹的稳定性和非线性系统的动力学特性,常作为判断Duffing系统混沌态和大尺度周期态的依据.根据Lyapunov指数的特征,Duffing系统的策动项采用正弦函数替代余弦函数方式,提出了一种基于QR分解的Duffing系统Lyapunov指数的求解方法.Matlab仿真结果表明了该算法的正确性、可靠性和有效性.

In order to compute the Lyapunov exponent of Duffing system,this paper adopts a kind of classical method based on QR decomposition to calculate the Lyapunov exponent of Duffing system.According to the basic characteristics of the Lyapunov exponent,we presents a kind of Lyapunov exponent algorithm based on QR decomposition for the known Duffing system.By using software simulation,we know that the Duffing system Lyapunov exponent algorithm based on QR decomposition is correctness.