Abstract
We study analytically the behavior of the largest Lyapunov exponent λ1 for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first-order-like or second-order phase transition depending on the ratio of two length scales: this is an excellent model to characterize λ1 as a dynamical indicator close to a phase transition.