On stochastization of one-dimensional chains of nonlinear oscillators

1. Fermi, Pasta, and Ulam performed in 1954 a series of numerical experiments aimed at ascertaining how randomization and the transition to a uniform en­ ergy distribution take place in dynamic systems with a large number of degrees of freedom[1,2]. The experi­ ment were performed on one-dimensional chains of nonlinear oscillators representing discrete models of a nonlinear string.The nonlinearity level and the num­ ber of oscillators were large enough (the chain con­ sisted of 64 oscillators in some experiments) for the experimenters to hope to discern rapid randomization of the chains and a transition to a uniform distribution of the energy over the degrees of freedom. They ob­ served instead a quasiperiodic energy exchange between several initially excited modes and were unable to ob­ serve a tendency to a stochastic transition of the energy to higher modes over a sufficiently large time (up to several hundred oscillation periods).