The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that coupled discrete-state noisy Markov units can be used to model mathematically more complex coupled noisy continuous phase oscillators. In this work we explore conditions that justify this assumption by coarse graining continuous phase units. In particular, we determine the minimum number of states necessary to justify this correspondence for Kuramoto-like oscillators.
Bibliographical noteFunding Information:
D.E. thanks FONDECYT Project No. 1140128 for financial support. A.R. acknowledges Capes for its support (Grant No. 99999.000296/2015-05). K.L. acknowledges the support of the ONR under Grant No. N00014-13-1-0205. R.T. acknowledges FEDER (European Union) and MINECO (Spain) under Grant No. ESOTECOS FIS2015-63628-C2-R.
© 2016 American Physical Society.