The so-called "Kuramoto models" and similar ones represent a paradigmatic way to describe a number of synchronization phenomena. These are states into which incoherent systems may go, often as it occurs in phase transition, and concern a variety of cases, ranging form Physics to Neuroscience, from Biology to Engineering and even Social Sciences. They explain, at least qualitatively, a large variety of complex processes. In this paper, we review such models and the underlying mathematics, showing some of their peculiarities.
I cosiddetti "modelli di Kuramoto", e altri simili ad essi, rappresentano un modo paradigmatico per descrivere una serie di fenomeni di sincronizzazione, cioè stati a cui possono passare sistemi incoerenti, come capita spesso nelle transizioni di fase e in una moltitudine di casi, che vanno dalla Fisica alle Neuroscienze, dalla Biologia all'Ingegneria e persino alle Scienze Sociali. Questi fenomeni spiegano, almeno qualitativamente, una grande varietà di processi complessi. In questo articolo, passiamo in rassegna tali modelli e la matematica sottostante, mostrando alcune delle loro peculiarità
@article{RUMI_2016_1_1_2_123_0,
author = {Renato Spigler},
title = {The mathematics of Kuramoto models which describe synchronization phenomena},
journal = {Matematica, Cultura e Societ\`a. Rivista dell'Unione Matematica Italiana},
volume = {1},
year = {2016},
pages = {123-132},
mrnumber = {3586455},
language = {en},
url = {http://dml.mathdoc.fr/item/RUMI_2016_1_1_2_123_0}
}
Spigler, Renato. The mathematics of Kuramoto models which describe synchronization phenomena. Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana, Tome 1 (2016) pp. 123-132. http://gdmltest.u-ga.fr/item/RUMI_2016_1_1_2_123_0/
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