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

F. Cecconi·A. Politi
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Abstract

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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F. Cecconi, A. Politi. 1998-09-11. N-tree approximation for the largest Lyapunov exponent of a coupled-map lattice. https://doi.org/10.1103/physreve.56.4998

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