Multibranch entrainment and slow evolution among branches in coupled oscillators

Details Multibranch entrainment and slow evolution among branches in coupled oscillators Multibranch entrainment and slow evolution among branches in coupled oscillators

2001-04-27

arxiv.org/abs/cond-mat/0104526v4

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.88.024102

In globally coupled oscillators, it is believed that strong higher harmonics of coupling functions are essential for multibranch entrainment (MBE), in which there exist many stable states, whose number scales as $\sim$ $O(\exp N)$ (where N is the system size). The existence of MBE implies the non-ergodicity of the system. Then, because this apparent breaking of ergodicity is caused by microscopic energy barriers, this seems to be in conflict with a basic principle of statistical physics. In this paper, using macroscopic dynamical theories, we demonstrate that there is no such ergodicity breaking, and such a system slowly evolves among branch states, jumping over microscopic energy barriers due to the influence of thermal noise. This phenomenon can be regarded as an example of slow dynamics driven by a perturbation along a neutrally stable manifold consisting of an infinite number of branch states.

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