Synchronization of oscillators coupled through an environment

Abstract

We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate synchronization of systems of oscillators which are weakly coupled, in the sense that the influence of the oscillators on the environment is weak. We prove that arbitrarily weak coupling will synchronize the oscillators, provided that this coupling is of the 'right' sign. We illustrate our general results by applications to a model of coupled GnRH neuron oscillators proposed by Khadra and Li [14], and to indirectly weakly-coupled λ − ω oscillators.

Coupling-induced synchronization in multicellular circadian oscillators of mammals

“…Katriel G. have proved the synchronization of oscillators coupled through an environment (Katriel 2008). According to the conclusion of (Katriel 2008), if Eq.…”

“…Thus, according to the conclusion of (Katriel 2008), the oscillators can achieve synchronization with appropriate parameter values.…”

Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment

“…Such a coupling configuration which could, to some extent, mimic physiological processes has recently been studied in other contexts, ranging from different forms of synchronization to amplitude death [37][38][39][40][49][50][51]. Physiological processes are well known to be dynamic.…”

“…In some microscopic systems, however, the interaction is not direct [29][30][31][32][33][34][35][36]. For instance, populations of cells in which oscillatory reactions occur (e.g., as in circadian rhythms), communicate via chemicals that diffuse in the surrounding medium [29,31,32,[37][38][39][40]. Similarly, suspensions of yeast in nutrient solutions may undergo transitions to coordinated activity that are also believed to arise through communication via chemicals diffusing in the surrounding medium [35,39].…”

“…For instance, populations of cells in which oscillatory reactions occur (e.g., as in circadian rhythms), communicate via chemicals that diffuse in the surrounding medium [29,31,32,[37][38][39][40]. Similarly, suspensions of yeast in nutrient solutions may undergo transitions to coordinated activity that are also believed to arise through communication via chemicals diffusing in the surrounding medium [35,39]. Within an environment that may be changing, the ability to communicate between cells is an absolute requirement to ensure appropriate and robust coordination of their activities at all levels of the organism.…”