Synchronization in network geometries with finite spectral dimension Torres Agudo, Joaquín Bianconi, Ginestra Millán Vidal, Ana Paula Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and its dynamics. Specifically we explore the role of the spectral dimension in determining the synchronization properties of the Kuramoto model. We show that the synchronized phase can only be thermodynamically stable for spectral dimensions above four and that phase entrainment of the oscillators can only be found for spectral dimensions greater than two. We numerically test our analytical predictions on the recently introduced model of network geometry called complex network manifolds, which displays a tunable spectral dimension. 2021-10-04T10:31:30Z 2021-10-04T10:31:30Z 2019-02 info:eu-repo/semantics/article Torres, JJ; Bianconi, G; Millán, AP. Synchronization in network geometries with finite spectral dimension. PHYSICAL REVIEW E 99(2) http://hdl.handle.net/10481/70614 10.1103/PhysRevE.99.022307 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España