WebIn Mathematics the Lyapunov exponent of a dynamical systems is a quantity that characterizes the rate of separation of infinitesimally close trajectories. Is there some new algorithms for... WebLyapunov指数是衡量系统动力学特性的一个重要定量指标,它表征了系统在相空间中相邻轨道间收敛或发散的平均指数率。对于系统是否存在动力学混沌, 可以从最大Lyapunov指 …

Chapter 7 Lyapunov Exponents - California Institute of …

WebJun 10, 2024 · 毕业设计（论文）-基于lyapunov指数的时间序列预测方法的研究.doc,沈阳航空工业学院毕业设计论文 PAGE PAGE 34 第1章 绪论 1.1 混沌的基本概念和特征 混沌是“确定的非线性系统所表现出来的内在随机性”。即混沌是系统固有的，系统所表现出来的复杂性是系统自身的、内在的因素造成的，并不是在外界 ... WebApr 13, 2008 · % 初始化三个Lyapunov指数 Lyapunov1 = zeros (iteratetimes,1); Lyapunov2 = zeros (iteratetimes,1); Lyapunov3 = zeros (iteratetimes,1); for i=1:iteratetimes tspan = tstart:tstep: (tstart + tstep*steps); [T,Y] = ode45 ('Rossler_ly', tspan, y); % 取积分得到的最后一个时刻的值 y = Y (size (Y,1),:); % 重新定义起始时刻 tstart = tstart + tstep*steps; y0 = … marine corps military records

Lyapunov指数计算_百度文库

WebA.M. Lyapunovproved that if the system of the first approximation is regular (e.g., all systems with constant and periodic coefficients are regular) and its largest Lyapunov exponent is negative, then the solution of the original system is asymptotically Lyapunov stable. The maximal Lyapunov exponent can be defined as follows: 1. λ = lim t → ∞ lim δ Z 0 → 0 1 t ln ⁡ δ Z ( t ) δ Z 0 {\displaystyle \lambda =\lim _{t\to \infty }\lim … See more For a dynamical system with evolution equation x ˙ i = f i ( x ) {\displaystyle {\dot {x}}_{i}=f_{i}(x)} in an n–dimensional phase space, the spectrum of … See more To introduce Lyapunov exponent consider a fundamental matrixX ( t ) {\displaystyle X(t)} (e.g., for linearization along a stationary solution x 0 {\displaystyle … See more If the system is conservative (i.e., there is no dissipation), a volume element of the phase space will stay the same along a trajectory. Thus the sum of all … See more The Lyapunov spectrum can be used to give an estimate of the rate of entropy production,of the fractal dimension, and of the Hausdorff dimension of the considered … See more WebLyapunov Exponents The Lyapunov exponent is a simple way to characterize the dynamics of a chaotic system by looking at the e ective degrees of freedom of the … nature based cities