Search results
Results From The WOW.Com Content Network
"Matlab Code for Lyapunov Exponents of Fractional-Order Systems". ... the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity ...
Python code for point trajectories [ edit ] import math import matplotlib.pyplot as plt import numpy as np def main ( u : float , points = 200 , iterations = 1000 , nlim = 20 , limit = False , title = True ): """ Args: u:float ikeda parameter points:int number of starting points iterations:int number of iterations nlim:int plot these many last ...
The classic way of computing Lyapunov exponents is solving a linear differential equation for the linearized flow map (). A more expedient approach is to compute the FTLE field from a simple finite-difference approximation to the deformation gradient. [ 2 ]
The divergence can have the trend of the positive maximal Lyapunov exponent, but not more. Moreover, also RPs of white noise processes can have a really long diagonal line, although very seldom, just by a finite probability. Therefore, the divergence cannot reflect the maximal Lyapunov exponent.
Download QR code; Print/export ... Notice the drastic change in the solutions with respect to the solution obtained with MATLAB. ... The Lyapunov exponents, ...
The master stability function is now defined as the function which maps the complex number to the greatest Lyapunov exponent of the equation y ˙ = ( D f + γ D g ) y . {\displaystyle {\dot {y}}=(Df+\gamma Dg)y.}
At this time, the Lyapunov exponent λ is maximized, and the state is the most chaotic. The value of λ for the logistic map at r = 4 can be calculated precisely, and its value is λ = log 2. Although a strict mathematical definition of chaos has not yet been unified, it can be shown that the logistic map with r = 4 is chaotic on [0, 1 ...
The values of the Lyapunov exponents are invariant with respect to a wide range of coordinate transformations. Suppose that g : X → X is a one-to-one map such that ∂ g / ∂ x {\displaystyle \partial g/\partial x} and its inverse exist; then the values of the Lyapunov exponents do not change.