Synchronization of oscillators coupled through an environment

Details Synchronization of oscillators coupled through an environment Synchronization of oscillators coupled through an environment

2008-04-23

arxiv.org/abs/0804.3734v1

Physica D: Nonlinear Phenomena 237 (2008), 2933-2944

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Scientific paper

10.1016/j.physd.2008.04.015

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, and to indirectly weakly-coupled lambda-omega oscillators

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