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Maximal Lyapunov exponent at crises (1996)
| Venue: | Phys. Rev. E |
| Citations: | 1 - 0 self |
BibTeX
@ARTICLE{Mehra96maximallyapunov,
author = {Vishal Mehra and Ramakrishna Ramaswamy},
title = {Maximal Lyapunov exponent at crises},
journal = {Phys. Rev. E},
year = {1996},
pages = {3420--3424}
}
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Abstract
We study the variation of Lyapunov exponents of simple dynamical systems near attractor-widening and attractor-merging crises. The largest Lyapunov exponent has universal behaviour, showing abrupt variation as a function of the control parameter as the system passes through the crisis point, either in the value itself, in the case of the attractor-widening crisis, or in the slope, for attractor merging crises. The distribution of local Lyapunov exponents is very different for the two cases: the fluctuations remain constant through a merging crisis, but there is a dramatic increase in the fluctuations at a widening crisis. In this paper, we study the behaviour of the Lyapunov exponent in systems where there are abrupt changes in the dynamics as a parameter is varied. Our interest is in exploring the typical dependence of the maximal Lyapunov exponent (MLE) on the control parameter so as to elucidate the signature of
Keyphrases
maximal lyapunov exponent lyapunov exponent control parameter widening crisis crisis point merging crisis attractor merging crisis universal behaviour abrupt change attractor-widening crisis abrupt variation local lyapunov exponent dramatic increase attractor-merging crisis typical dependence simple dynamical system
