Phase synchronization

{{Hatnote|For other types of Synchronization, see Synchronization (disambiguation).}} {{no footnotes|date=June 2017}} '''Phase synchronization''' is the process by which two or more cyclic signals tend to oscillate with a repeating sequence of relative phase angles.

Phase synchronisation is usually applied to two waveforms of the same frequency with identical phase angles with each cycle. However it can be applied if there is an integer relationship of frequency, such that the cyclic signals share a repeating sequence of phase angles over consecutive cycles. These integer relationships are called Arnold tongues which follow from bifurcation of the circle map.

One example of phase synchronization of multiple oscillators can be seen in the behavior of Southeast Asian fireflies <ref>{{Cite book |last=Strogatz |first=Steven |title=Sync: The Emerging Science of Spontaneous Order |publisher=Grand Central Publishing |year=2003 |isbn=978-0-7868-6844-5}}</ref><ref>{{Cite book |last1=Pikovsky |first1=Arkady |url=https://www.cambridge.org/core/books/synchronization/E46C1FC3ADC82EEA75AE6F5B9B74E28C |title=Synchronization: A Universal Concept in Nonlinear Sciences |last2=Rosenblum |first2=Michael |last3=Kurths |first3=Jürgen |date=2001 |publisher=Cambridge University Press |isbn=978-0-521-53352-2 |series=Cambridge Nonlinear Science Series |location=Cambridge}}</ref>. At dusk, the flies begin to flash periodically with random phases and a gaussian distribution of native frequencies. As night falls, the flies, sensitive to one another's behavior, begin to synchronize their flashing. After some time all the fireflies within a given tree (or even larger area) will begin to flash simultaneously in a burst.

Thinking of the fireflies as biological oscillators, we can define the phase to be 0° during the flash and +-180° exactly halfway until the next flash. Thus, when they begin to flash in unison, they synchronize in phase.

Phase synchronization patterns (n:m synchronization) have been also observed in the interaction of physiological and organ systems, for example in maternal-fetal cardiac phase-synchronization <ref>{{Cite journal |last1=Van Leeuwen |first1=P. |last2=Geue |first2=D. |last3=Thiel |first3=M. |last4=Cysarz |first4=D. |last5=Lange |first5=S. |last6=Romano |first6=M. C. |last7=Wessel |first7=N. |last8=Kurths |first8=J. |last9=Grönemeyer |first9=D. H. |date=2009-08-18 |title=Influence of paced maternal breathing on fetal-maternal heart rate coordination |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=106 |issue=33 |pages=13661–13666 |doi=10.1073/pnas.0901049106 |issn=1091-6490 |pmc=2728950 |pmid=19597150 |doi-access=free}}</ref><ref>{{Cite journal |last1=Ivanov |first1=Plamen Ch. |last2=Ma |first2=Qianli D. Y. |last3=Bartsch |first3=Ronny P. |date=2009 |title=Maternal–fetal heartbeat phase synchronization |journal=Proceedings of the National Academy of Sciences |volume=106 |issue=33 |pages=13641–13642 |bibcode=2009PNAS..10613641I |doi=10.1073/pnas.0906987106 |pmc=2728945 |pmid=19706494 |doi-access=free}}</ref>, brain blood flow velocity vs. peripheral blood pressure in stroke <ref>{{Cite journal |last1=Chen |first1=Zhi |last2=Hu |first2=Kun |last3=Stanley |first3=H. Eugene |last4=Novak |first4=Vera |last5=Ivanov |first5=Plamen Ch |date=March 2006 |title=Cross-correlation of instantaneous phase increments in pressure-flow fluctuations: applications to cerebral autoregulation |journal= Physical Review E|volume=73 |issue=3 Pt 1 |article-number=031915 |doi=10.1103/PhysRevE.73.031915 |issn=1539-3755 |pmc=2140229 |pmid=16605566 |arxiv=physics/0508102 |bibcode=2006PhRvE..73c1915C }}</ref>, cortico-muscular <ref>{{Cite journal |last1=Tass |first1=P. |last2=Rosenblum |first2=M. G. |last3=Weule |first3=J. |last4=Kurths |first4=J. |last5=Pikovsky |first5=A. |last6=Volkmann |first6=J. |last7=Schnitzler |first7=A. |last8=Freund |first8=H.-J. |date=1998-10-12 |title=Detection of n: m Phase Locking from Noisy Data: Application to Magnetoencephalography |url=https://link.aps.org/doi/10.1103/PhysRevLett.81.3291 |journal=Physical Review Letters |language=en |volume=81 |issue=15 |pages=3291–3294 |doi=10.1103/PhysRevLett.81.3291 |bibcode=1998PhRvL..81.3291T |issn=0031-9007|url-access=subscription }}</ref> and cardio-respiratory <ref>{{Cite journal |last1=Schäfer |first1=Carsten |last2=Rosenblum |first2=Michael G. |last3=Kurths |first3=Jürgen |last4=Abel |first4=Hans-Henning |date=1998 |title=Heartbeat synchronized with ventilation |url=https://www.nature.com/articles/32567 |journal=Nature |language=en |volume=392 |issue=6673 |pages=239–240 |doi=10.1038/32567 |pmid=9521318 |bibcode=1998Natur.392..239S |issn=1476-4687}}</ref><ref name=":0">{{Cite journal |last1=Bartsch |first1=Ronny P. |last2=Schumann |first2=Aicko Y. |last3=Kantelhardt |first3=Jan W. |last4=Penzel |first4=Thomas |last5=Ivanov |first5=Plamen Ch. |date=2012-06-26 |title=Phase transitions in physiologic coupling |journal=Proceedings of the National Academy of Sciences |volume=109 |issue=26 |pages=10181–10186 |doi=10.1073/pnas.1204568109 |doi-access=free |pmc=3387128 |pmid=22691492 |bibcode=2012PNAS..10910181B }}</ref> coupling with the degree of synchronization changing across physiological states (sleep/wake, sleep stages) and age groups <ref name=":0" /><ref>{{Cite journal |last1=Bartsch |first1=Ronny P. |last2=Liu |first2=Kang Kl |last3=Ma |first3=Qianli Dy |last4=Ivanov |first4=Plamen Ch |date=2014 |title=Three Independent Forms of Cardio-Respiratory Coupling: Transitions across Sleep Stages |journal=Computing in Cardiology |volume=41 |pages=781–784 |issn=2325-8861 |pmc=4319215 |pmid=25664348}}</ref>.

One way to keep a local oscillator "phase synchronized" with a remote transmitter uses a phase-locked loop.

==References== Category:Wave mechanics Category:Synchronization <references />

==External links== A tutorial on calculating [https://www.nbtwiki.net/doku.php?id=tutorial:phase_locking_value Phase locking and Phase synchronization] in Matlab.