title: Synchronization of coupled noisy oscillators: Coarse graining from continuous to discrete phases.
abstract: 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.
authors.affiliation: Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Avenida Monseñor Álvaro del Portillo No. 12.455, Las Condes, Santiago, Chile.
authors.forename: Daniel
authors.initials: D
authors.lastname: Escaff
authors.affiliation: Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58059-900 João Pessoa, Brazil.
authors.forename: Alexandre
authors.initials: A
authors.lastname: Rosas
authors.affiliation: IFISC (Instituto de Física Interdisciplinaria y Sistemas Complejos), CSIC-UIB, E-07122 Palma de Mallorca, Spain.
authors.forename: Raúl
authors.initials: R
authors.lastname: Toral
authors.affiliation: Department of Chemistry and Biochemistry and BioCircuits Institute, University of California San Diego, La Jolla, California 92093-0340, USA.
authors.forename: Katja
authors.initials: K
authors.lastname: Lindenberg