We consider anti-phase synchronization of coupled oscillators using the Stuart-Landau model and explore its relative infrequency in occurrence compared to in-phase synchronization. We report effective limits in number of oscillators which can anti-phase synchronize for general configurations of real-world networks. We link anti-phase synchronization to the Ising model and consequently to combinatorial optimization problems, thereby explaining experimentally observed limits in self-organization of natural systems. We illustrate this using the Steiner-tree problem.
@article{arxiv.1908.07314,
title = {Effective Bounds on Network-Size for Anti-phase Synchronization},
author = {George Vathakkattil Joseph and Vikram Pakrashi},
journal= {arXiv preprint arXiv:1908.07314},
year = {2020}
}