Structure preserving schemes for the continuum Kuramoto model: Phase transitions
José A. CarrilloDepartment of Mathematics, Imperial College London, London SW7 2AZ, United KingdomYoung-Pil ChoiDepartment of Mathematics and Institute of Applied Mathematics, Inha University, Incheon, 402-751, Republic of KoreaLorenzo PareschiDepartment of Mathematics and Computer Science, University of Ferrara, Via N. Machiavelli 35, 44121, Ferrara, Italy
2018en
ABI
Abstract
The construction of numerical schemes for the Kuramoto model is challenging due to the structural properties of the system which are essential in order to capture the correct physical behavior, like the description of stationary states and phase transitions. Additional difficulties are represented by the high dimensionality of the problem in presence of multiple frequencies. In this paper, we develop numerical methods which are capable to preserve these structural properties of the Kuramoto equation in the presence of diffusion and to solve efficiently the multiple frequencies case. The novel schemes are then used to numerically investigate the phase transitions in the case of identical and nonidentical oscillators.
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