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

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

1998-09-11

arxiv.org/abs/cond-mat/9809177v1

Phys.Rev.E vol.56, 4998 (1997)

Physics

Condensed Matter

Disordered Systems and Neural Networks

RevTeX, 15 pages,5 figures

Scientific paper

10.1103/PhysRevE.56.4998

The N-tree approximation scheme, introduced in the context of random directed polymers, is here applied 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 $n$s. 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.

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