Numerical study of Lyapunov exponents for products of correlated random matrices
Abstract
We numerically study Lyapunov spectra and the maximal Lyapunov exponent (MLE) in products of real symplectic correlated random matrices, each of which is generated by a modified Bernoulli map. We can systematically investigate the influence of the correlation on the Lyapunov exponents because the statistical properties of the sequence generated by the map, whose correlation function shows powerlaw decay, have been well investigated. It is shown that the form of the scaled Lyapunov spectra does not change much even if the correlation of the sequence increases in the stationary region, and in the nonstationary region the forms are quite different from those obtained in the δcorrelated purely random case. The fluctuation strength dependence of the MLE changes with increasing correlation, and a different scaling law from that of the δcorrelated case can be observed in the nonstationary region. Moreover, the statistical properties of the probability distribution of the local Lyapunov exponents are quite different from those obtained from δcorrelated random matrices. Slower convergence that does not obey the centrallimit theorem is observed for increasing correlation.
 Publication:

Physical Review E
 Pub Date:
 February 2001
 DOI:
 10.1103/PhysRevE.63.026203
 Bibcode:
 2001PhRvE..63b6203Y
 Keywords:

 05.45.a;
 05.40.a;
 72.15.Rn;
 02.30.Xx;
 Nonlinear dynamics and chaos;
 Fluctuation phenomena random processes noise and Brownian motion;
 Localization effects;
 Calculus of variations