lyapExp = lyapunovExponent(X,fs,[],dim) lyapExp = lyapunovExponent(X,fs,lag,dim) [lyapExp,estep,ldiv] = lyapunovExponent(___) ___= lyapunovExponent(___,Name,Value) lyapunovExponent(___) Description lyapExp= lyapunovExponent(X,fs)estimates the Lyapunov exponent of the uniformly sampled ...
matlab计算李雅普诺夫指数 如何理解和计算Lyapunov exponent spectrum? 1、这是我听到最接近人话的描述。 混沌运动的基本特点是运动对初始条件极为敏感,两个极为靠近的初始值所产生的轨迹,随着时间推移将按照指数方式分离。李娜诺普指数就是描述这一现象的量。 2、 结论: --- --- 计算方法来了: 求解指数的这一...
Twitter Google Share on Facebook Lyapunov Exponents A measure of the dynamics of anattractor. Each dimension has a Lyapunov exponent. A positive exponent measures sensitive dependence on initial conditions, or how much our forecasts can diverge based upon different estimates of starting conditions. Ano...
The Lyapunov exponent has been investigated both numerically and analytically for various plasma states. With the use of a three-dimensional particle code that calculates Coulomb forces among individual particles, instantaneous expansion rates of nearby trajectories in a phase space are studied. It is ...
This code contains two functions (LE_XIE2006.m and MLE_XIE2009.m) which numerically assess the sample and p-th moment stability of a linear stochastic system driven by an ergodic process (), according to the largest Lyapunov exponent (LE) and moment Lyapunov exponents (MLE), respectiv...
In this article we study if a Deep Learning technique can be used to obtain an approximate value of the Lyapunov exponents of a dynamical system. Moreover, we want to know if Machine Learning techniques are able, once trained, to provide the full Lyapunov exponents spectrum with just single-...
sourcecode/math/detail150408.html recnstitution MATLAB程序如下: function [Texp,Lexp]=lyapunov(n,tstart,stept,tend,ystart,ioutp); global DS; global P; global calculation_progress first_call; global driver_window; global TRJ_bufer Time_bufer bufer_i; % % Lyapunov exponent calcullation for ...
% normalize exponent % rescale = 0; u1 =1.e10; u2 =-1.e10; for k=1:n_exp lp(k)=cum(k)/(t-tstart); % Plot Xd=get(PlotLyap{k},'Xdata'); Yd=get(PlotLyap{k},'Ydata'); if timeplot<t u1=min(u1,min(Yd)); u2=max(u2,max(Yd)); end; ...
The finite size Lyapunov exponent (FSLE) has been used extensively since the late 1990s to diagnose turbulent regimes from Lagrangian experiments and to detect Lagrangian coherent structures in geophysical flows and two-dimensional turbulence. Historically, the FSLE was defined in terms of its computat...
The Lyapunov exponent in Equation (1) is denoted by λ. Any positive value in the limit accounts for chaos in the system, while non-positive proves the regularity. There are many numerical methods of computing Lyapunov exponents, e.g., Wolf method, Rosenstein method, Kantz method, method ...