New phenomenon in the stochastic transition of coupled oscillators

We have performed a detailed numerical investigation around the region of transition from quasiperiodic to stochastic motions for a chain of particles with Lennard-Jones interaction. We have found that the curve for the stochastic parameter (or maximal Lyapunov characteristic number) as a function of energy presents successive bifurcations in that region, a phenomenon not yet observed in this field. This phenomenon is interpreted as indicating that the so-called stochastic region is in general subdivided into disjoint invariant components, which merge into a unique stochastic region as energy increases. © 1978 The American Physical Society.