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Published on: June 17, 2020
Phase definition to assess synchronization quality of nonlinear oscillators
Leandro Freitas1, Leonardo A B Torres2, Luis A Aguirre2
1Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerais, Campus Betim R. Itaguaçu 595, 32677-562 Betim, Minas Gerais, Brazil.
Abstract:
This 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.
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