Autowave processes in continual chains of unidirectionally coupled oscillators

Abstract

We introduce a mathematical model of a continual circular chain of unidirectionally coupled oscillators. It is a nonlinear hyperbolic boundary value problem obtained from a circular chain of unidirectionally coupled ordinary differential equations in the limit as the number of equations indefinitely increases. We study the attractors of this boundary value problem. Combining analytic and numerical methods, we establish that one of the following two alternatives takes place in this problem: either the buffer phenomenon (unbounded accumulation of stable periodic motions) or chaotic attractors of arbitrarily high Lyapunov dimensions.