Synchronization desynchronization transition

Soluble Many-Osdllator Model Showing Synchronization-Desynchronization Transitions... 

Synchronization or entrainment is a key concept to the understanding of selforganization phenomena occurring in the fields of coupled oscillators of the dissipative type. We may even say that Part II is devoted to the consideration of this single mode of motion in various physical situations. Specifically, Chap. 6 is concerned with wave phenomena and pattern formation, which may be viewed as typical synchronization phenomena in distributed systems. In contrast, we shall study in Chap. 7 turbulence in reaction-diffusion systems, which is caused by desynchronization among local oscillators. Chapter 5 deals with self-synchronization phenomena in the discrete populations of oscillators where the way they are distributed in physical space is not important (for reasons stated later). We shall introduce some kind of randonmess by assuming that the oscillators are either different in nature from each other or at best statistically identical. One may then expect phase-transition-like phenomena, characterized by the appearance or disappearance of collective oscillations in the oscillator communities. In describing such a new class of phase transitions. Method I turns out to be very useful. 

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