Phase definition to assess synchronization quality of nonlinear oscillators
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Universidade Federal de Minas Gerais
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Artigo de periódico
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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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Liapunov, Funções de, Processamento de sinais - Técnicas digitais
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Synchronization 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., Numerical 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., Phase synchronization is the process by which two or more cyclic signals tend to oscillate with a repeating sequence of relative phase angles.
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https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.052202