Phase definition to assess synchronization quality of nonlinear oscillators

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dc.creatorLeandro Freitas
dc.creatorLeonardo Antonio Borges Torres
dc.creatorLuis Antonio Aguirre
dc.date.accessioned2025-04-17T12:57:32Z
dc.date.accessioned2025-09-09T00:32:28Z
dc.date.available2025-04-17T12:57:32Z
dc.date.issued2018
dc.identifier.doihttps://doi.org/10.1103/PhysRevE.97.052202
dc.identifier.issn2470-0045
dc.identifier.urihttps://hdl.handle.net/1843/81684
dc.languageeng
dc.publisherUniversidade Federal de Minas Gerais
dc.relation.ispartofPhysical Review E
dc.rightsAcesso Restrito
dc.subjectLiapunov, Funções de
dc.subjectProcessamento de sinais - Técnicas digitais
dc.subject.otherSynchronization is a ubiquitous phenomenon which has been addressed with different approaches. A common approach is to reduce complex oscillators, such as living beings, to a phase model. This kind of method was successfully used to describe synchronization phenomena in biology, chemical oscillators, and many others, especially in large populations of oscillators.
dc.subject.otherNumerical results with cord and modified Hodgkin-Huxley oscillators showed that the VFP can be used to assess phase synchronization and provide information about the quality of the synchronization, beyond the binary status of yes-no phase sync. Simulations showed that the VFP can be applied when the vector field is unknown and when only one state variable is available. An example with coupled hyperchaotic Rössler oscillators showed that similar results can be obtained for other classes of oscillators.
dc.subject.otherPhase synchronization is the process by which two or more cyclic signals tend to oscillate with a repeating sequence of relative phase angles.
dc.titlePhase definition to assess synchronization quality of nonlinear oscillators
dc.typeArtigo de periódico
local.citation.issue5
local.citation.spage052202
local.citation.volume97
local.description.resumoThis paper proposes a phase definition, named the vector field phase, which can be defined for systems with arbitrary finite dimension and is a monotonically increasing function of time. The proposed definition can properly quantify the dynamics in the flow direction, often associated with the null Lyapunov exponent. Numerical examples that use benchmark periodic and chaotic oscillators are discussed to illustrate some of the main features of the definition, which are that (i) phase information can be obtained either from the vector field or from a time series, (ii) it permits not only detection of phase synchronization but also quantification of it, and (iii) it can be used in the phase synchronization of very different oscillators.
local.publisher.countryBrasil
local.publisher.departmentENG - DEPARTAMENTO DE ENGENHARIA ELETRÔNICA
local.publisher.initialsUFMG
local.url.externahttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.052202

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