SCALING-LAW FOR THE MAXIMAL LYAPUNOV EXPONENT

R LIVI, A POLITI, S RUFFO

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We study the scaling law for epsilon --> 0 of the maximal Lyapunov exponent for coupled chaotic map lattices and for products of random Jacobi matrices. To this purpose we develop approximate analytical treatments of the random matrix problem inspired by the theory of directed polymers in a random medium: a type of mean-field method and a tree approximation which introduces correlations. The theoretical results suggest a leading \log epsilon\-1 increase in the maximal Lyapunov exponent near epsilon = 0, which is confirmed by numerical simulations, also for coupled map lattices. A dynamical mechanism responsible for this behaviour is investigated for a 2 x 2 random matrix model. The theory also predicts a phase transition at a critical value of the coupling epsilon(c), which is not observed in numerical simulations and might be an artifact of the approximation.

Original languageEnglish
Pages (from-to)4813-4826
Number of pages14
JournalJournal of Physics A: Mathematical and General
Volume25
Issue number18
Publication statusPublished - 21 Sep 1992

Keywords

  • COUPLED MAP LATTICES
  • SPATIOTEMPORAL INTERMITTENCY
  • DIRECTED POLYMERS
  • SYSTEMS
  • CHAOS

Cite this

SCALING-LAW FOR THE MAXIMAL LYAPUNOV EXPONENT. / LIVI, R ; POLITI, A ; RUFFO, S .

In: Journal of Physics A: Mathematical and General, Vol. 25, No. 18, 21.09.1992, p. 4813-4826.

Research output: Contribution to journalArticle

LIVI, R ; POLITI, A ; RUFFO, S . / SCALING-LAW FOR THE MAXIMAL LYAPUNOV EXPONENT. In: Journal of Physics A: Mathematical and General. 1992 ; Vol. 25, No. 18. pp. 4813-4826.
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KW - SYSTEMS

KW - CHAOS

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