n-tree approximation for the largest Lyapunov exponent of a coupled-map lattice

Year: 1997

Authors: Cecconi F., Politi A.

Autors Affiliation: Dipartimento di Fisica, Università di Firenze, 50125 Firenze, Italy;
Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, 50125 Firenze, Italy;
Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy

Abstract: The n-tree approximation scheme, introduced in the context of random directed polymers, is applied here to the computation of the maximum Lyapunov exponent in a coupled-map lattice. We discuss both an exact implementation for small tree depth n and a numerical implementation for larger n. We find that the phase transition predicted by the mean-field approach shifts towards larger values of the coupling parameter when the depth n is increased. We conjecture that the transition eventually disappears.

Journal/Review: PHYSICAL REVIEW E

Volume: 56 (5)      Pages from: 4998  to: 5003

KeyWords: Directed Polymers; 1/d Expansion; Chaos; Systems
DOI: 10.1103/PhysRevE.56.4998

Citations: 6
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