DYNAMICS OF THE NONPERIODIC DISCRETE SELF-TRAPPING EQUATION

We study the dynamics of a version of the discrete self-trapping equation which describes an array of three nonlinear oscillators with nearest neighbor coupling. The reduced symmetry of this system compared to the usual system with periodic boundary conditions leads to some interesting effects which are not present in the higher symmetry case. We calculate the Lyapunov exponents for a wide variety of initial conditions, and examine some of the self-trapping properties of this particular system. We find that self-trapping of the excitation can occur on one or two of the three oscillators, and that the stability properties of certain stationary solutions extend to broad areas of neighboring trajectories in phase space.