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Updated: Dec 24, 2025
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Phase coherence is not related to topology
Leandro Freitas1, Leonardo L Portes, Leonardo A B Torres
1Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerais, Campus Betim Rua Itaguaçu 595, 32.677-562 Betim, MG, Brazil.
Abstract:
Phase coherence is an important measure in nonlinear science. Whereas there is no generally accepted definition for phase and therefore for phase coherence, many works associate this feature with topological aspects of the systems, such as having a well-defined rotating center. Given the relevance of this concept for synchronization problems, one aim of this paper is to argue by means of a couple of counterexamples that phase coherence is not related to the topology of the attractor. A second aim is to introduce a phase-coherence measure based on recurrence plots, for which probabilities of recurrences for two different trajectories are similar for a phase-coherent system and dissimilar for non-phase-coherent systems. The measure does not require a phase variable defined a priori.
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