Synchronization of oscillators coupled through an environment

摘要: Abstract We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. give criteria for the stability or instability a synchronized oscillation. Using these we investigate systems which weakly coupled, in sense influence on environment is weak. prove arbitrarily weak coupling will synchronize oscillators, provided this ‘right’ sign. illustrate our general results by applications to model GnRH neuron proposed Khadra and Li [A. Khadra, Y.X. Li, A pulsatile secretion gonadotropin-releasing hormone from hypothalamic neurons, Biophys. J. 91 (2006) 74–83.], weakly-coupled λ – ω oscillators.