preprint: paper on coupled oscillator systems

[Toru Aonishi]

Dear Connectionists,

We are pleased to announce the availability of our recent paper
and of two potentially related papers.

Recent paper:
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Acceleration effect of coupled oscillator systems

T. Aonishi, K. Kurata and M. Okada, Physical Review E (in press)

Available at

    http://arXiv.org/abs/cond-mat/0201453

Abstract:

We have developed a curved isochron clock (CIC) by modifying the
radial isochron clock to provide a clean example of the acceleration
(deceleration) effect. By analyzing a two-body system of coupled CICs,
we determined that an unbalanced mutual interaction caused by curved
isochron sets is the minimum mechanism needed for generating the
acceleration (deceleration) effect in coupled oscillator systems. From
this we can see that the Sakaguchi and Kuramoto (SK) model which is a
class of non-frustrated mean feild model has an acceleration
(deceleration) effect mechanism. To study frustrated coupled
oscillator systems, we extended the SK model to two oscillator
associative memory models, one with symmetric and one with asymmetric
dilution of coupling, which also have the minimum mechanism of the
acceleration (deceleration) effect. We theoretically found that the
{\it Onsager reaction term} (ORT), which is unique to frustrated
systems, plays an important role in the acceleration (deceleration)
effect. These two models are ideal for evaluating the effect of the
ORT because, with the exception of the ORT, they have the same order
parameter equations. We found that the two models have identical
macroscopic properties, except for the acceleration effect caused by
the ORT. By comparing the results of the two models, we can extract
the effect of the ORT from only the rotation speeds of the oscillators.

Related papers:
--------------

Multibranch entrainment and slow evolution among branches in coupled
oscillators

T. Aonishi and M. Okada, Physical Review Letters, 88[2], 024102 (2002) 

Available at

    http://prl.aps.org/ 
    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.

----

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/