Editing Synchronization (section)

== Dynamical systems ==
[[File:Wesphysdemo - Synchronized Metronomes.webm|thumb|275px|A mechanical demonstration of synchronization of oscillators: [[metronome]]s, initially out of phase, synchronize through small motions of the base on which they are placed]]
{{See also|Synchronization of chaos}}

Synchronization of multiple interacting [[dynamical system]]s can occur when the systems are [[Self-oscillation|autonomous oscillators]]. Poincaré phase oscillators are model systems that can interact and partially synchronize within random or regular networks.<ref name="Nolte">{{cite book | first = David | last = Nolte | title = Introduction to Modern Dynamics: Chaos, Networks, Space and Time  | publisher = [[Oxford University Press]] |  year = 2015 }}</ref> In the case of global synchronization of phase oscillators, an abrupt transition from unsynchronized to full synchronization takes place when the coupling strength exceeds a critical threshold. This is known as the [[Kuramoto model]] [[phase transition]].<ref name=":1">{{Cite web|url=https://www.youtube.com/watch?v=t-_VPRCtiUg|title = The Surprising Secret of Synchronization|website = [[YouTube]]| date=31 March 2021 }}</ref> Synchronization is an emergent property that occurs in a broad range of dynamical systems, including neural signaling, the beating of the heart and the synchronization of fire-fly light waves. A unified approach that quantifies synchronization in chaotic systems can be derived from the statistical analysis of measured data.<ref> {{Cite journal|last1=Shah|first1=Dipal| last2=Springer|first2=Sebastian|last3=Haario|first3=Heikki|last4=Barbiellini|first4=Bernardo|last5=Kalachev|first5=Leonid|date=2023|title= Data based quantification of synchronization|journal=Foundations of Data Science|volume=5|issue=1|pages=152–176|doi=10.3934/fods.2022020|doi-access=free}}</ref>