Papers on coupled oscillators

[Toru Aonishi]

Dear Connectionists,

I am pleased to announce the availability of my recent paper
and of one potentially related paper.

Recent paper:
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Multibranch entrainment and slow evolution among branches in coupled
oscillators

T. Aonishi and M. Okada, Physical Review Letters (in press)

Available at

http://arXiv.org/abs/cond-mat/0104526 

Abstract:

In globally coupled oscillators, it is believed that strong higher
harmonics of coupling functions are essential for {\it 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 {\it
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.

Related paper:
--------------

Statistical mechanics of an oscillator associative memory with
scattered natural frequencies

T. Aonishi, K. Kurata and M. Okada, Physical Review Letters, 82[13],
pp. 2800--2803 (1999) 

Available at

http://prl.aps.org/ 
http://arXiv.org/abs/cond-mat/9808090

Abstract:

Analytic treatment of a non-equilibrium random system with large
degrees of freedoms is one of most important problems of
physics. However, little research has been done on this problem as far
as we know. In this paper, we propose a new mean field theory that can
treat a general class of a non-equilibrium random system. We apply the
present theory to an analysis for an associative memory with
oscillatory elements, which is a well-known typical random system with
large degrees of freedoms. 

Regards,

Toru Aonishi (Ph.D)

Laboratory for Advanced Brain Signal Processing
Brain Science Institute 
The Institute of Physical and Chemical Research (RIKEN) 
Hirosawa, 2-1, Wako-shi, Saitama, 351-0198, Japan 
E-mail: aonishi at brain.riken.go.jp
URL: http://www.bsp.brain.riken.go.jp/~aonishi/