Collective Dynamics of Two-Mode Stochastic Oscillators

Abstract

We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the parameter space the periodicity of the collective output is enhanced by the considered coupling. This system can be used as a new model to describe synchronization-like phenomena in systems of units with two or more oscillation modes. The model can also explain how periodic dynamics can be generated by coupling largely stochastic units. Similar systems could be responsible for the emergence of rhythmic behavior in complex biological or sociological systems.

Emergent synchronisation properties of a refrigerator demand side management system

“…A relation with the Kuramoto and Nikitin models [15,16], which are models for the behaviour of a large set of nearly identical coupled oscillators, would be worth to study.…”

Delay-Induced Excitability

“…Both curves are qualitatively similar and show their maxima close to odd multiples of and minima at even multiples of . However, it must be noted that, while for the discrete model the coherence is an increasing function with noise [12,19], for the continuous model it is maximized for a finite noise strength, due to the inherent stochastic nature of all transitions involved. Excitability has been observed in the intensity of semiconductor lasers with optical feedback [21].…”

“…Our system can be seen as a continuous realization of a discrete three-state model [12,19], in which only the firing transition is stochastic. The refractory state is split into two states, and the transition between these two states as well as the transition back into the resting state are deterministic The inset shows the change in slope at T 2 for particles in the left well, which is due to a higher order effect in the feedback strength [16].…”

Synchronization of flashing electronic oscillators

“…Models that aim to describe realistically such systems should take this differences into consideration and should consider a complex interdisciplinary approach stepping over the simple picture of interacting mechanical oscillators. A recently introduced synchronization model [5], proposed that synchronization might arise also as a byproduct of some complex optimization procedure. Therefore, models that aim to describe realistically such systems should take this possibility into consideration and step over the simple physical models offered by interacting mechanical oscillators.…”