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Title: Cartesian product of synchronization transitions and hysteresis
Authors: Wang, C.Zou, Y.Guan, S.Kurths, J.
Publishers Version:
Issue Date: 2017
Published in: New Journal of Physics Vol. 19 (2017), No. 12
Publisher: Bristol : Institute of Physics Publishing
Abstract: We present theoretical results when applying the Cartesian product of two Kuramoto models on different network topologies. By a detailed mathematical analysis, we prove that the dynamics on the Cartesian product graph can be described by the canonical equations as the Kuramoto model. We show that the order parameter of the Cartesian product is the product of the order parameters of the factors. On the product graph, we observe either continuous or discontinuous synchronization transitions. In addition, under certain conditions, the transition from an initially incoherent state to a coherent one is discontinuous, while the transition from a coherent state to an incoherent one is continuous, presenting a mixture state of first and second order synchronization transitions. Our numerical results are in a good agreement with the theoretical predictions. These results provide new insight for network design and synchronization control.
Keywords: Cartesian product graphs; hysteresis; Kuramoto model; synchronization transition; Hysteresis; Set theory; Canonical equations; Cartesian product graph; Cartesian Products; Kuramoto models; Mathematical analysis; Numerical results; Synchronization control; Synchronization transitions; Synchronization
DDC: 530
License: CC BY 3.0 Unported
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