http://scholarpedia.org/article/Lyapunov_exponent Splet28. apr. 2024 · Download PDF Abstract: We show that the Lyapunov exponents of a periodic orbit can be easily obtained from the eigenvalues of the monodromy matrix. It turns out …

How to calculate Lyapunov exponent for 1D chaotic map? Part 1

SpletThe conception “Lyapunov Exponent” has been used widely in the study of dynamical system. Usually, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories Z(t) and Z 0 (t) in phase space. Let GZ (t) Z (t)-Z 0 (t), SpletThe Lyapunov exponent is then an even function of x. We report results for both polynomial tting and Gaussian process tting. 3.1 Polynomial tting To ensure that the tting function is an even function of xwe make F an even function and ˚an odd function. Both F and ˚are expanded in Taylor series. The series are truncated at orders nand m tara singh berkeley

Lyapunov exponents for the double pendulum and their fractal …

Splet16. jun. 2024 · Nolds provides the algorithm of Rosenstein et al. (lyap_r) to estimate the largest Lyapunov exponent and the algorithm of Eckmann et al. (lyap_e) to estimate the … 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 _{ \delta \mathbf {Z} _{0} \to 0}{\frac {1}{t}}\ln {\frac { \delta \mathbf {Z} (t) }{ \delta \mathbf {Z} _{0} }}} The limit δ Z 0 → 0 {\displaystyle \delta … Prikaži več 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 … Prikaži več To introduce Lyapunov exponent consider a fundamental matrixX ( t ) {\displaystyle X(t)} (e.g., for linearization along a stationary solution x 0 {\displaystyle … Prikaži več 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 … Prikaži več 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 … Prikaži več tara singer