Nonlinear Waves and Moving Clusters on Rings

Abstract

The dynamics of a ring of masses including dissipative forces (passive and active friction) and Toda interactions between the masses are investigated. The characteristic attractor structure and the influence of noise by coupling to a heat bath are studied. The system may be driven from the thermodynamic equilibrium to far from equilibrium states by including negative friction. We show, that over-critical pumping with free energy may lead to a partition of the phase space into attractor regions corresponding to several types of collective motions including uniform rotations, one- and multiple soliton excitations and relative oscillations. With Lennard-Jones like interaction potentials the particles form clusters moving along the ring.