Limits on Anti-Phase Synchronization in Oscillator Networks

• Published in: Scientific reports Vol. 10; no. 1; p. 10178
• Main Authors: Vathakkattil Joseph, George, Pakrashi, Vikram
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 23.06.2020; Nature Publishing Group; Nature Portfolio
• Subjects: 639/705/1041; 639/766/530/2801; 639/766/530/2803; Algorithms; Connectivity; Graphs; Humanities and Social Sciences; Lasers; multidisciplinary; Neural networks; Oscillators; Science; Science (multidisciplinary); Synchronization
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-020-67021-6

Anti-phase synchronization is the spontaneous formation of 2 clusters of oscillators synchronized between themselves within a cluster but opposite in phase with the other cluster. Neuronal networks in human and animal brains, ecological networks, climactic networks, and lasers are all systems that exhibit anti-phase synchronization although the phenomenon is encountered less frequently than the celebrated in-phase synchronization. We show that this disparity in occurrence is due to fundamental limits on the size of networks that can sustain anti-phase synchronization. We study the influence of network structure and coupling conditions on anti-phase synchronization in networks composed of coupled Stuart-Landau oscillators. The dependence of probability of anti-phase synchronization on connectivity of the network, strength of interaction over distance, and symmetry of the network is illustrated. Regardless of favourable network conditions, we show that anti-phase synchronization is limited to small networks, typically smaller than 20 nodes .