Synchronization in asymmetrically coupled networks with homogeneous oscillators

Synchronization among coupled oscillators is a common feature of symmetrically coupled networks with homogeneous, i.e., identical, oscillators. Recently, it was reported [T. Nishikawa and A. Motter, Phys. Rev. Lett. 117. 114101 (2016) and Y. Zhang, T. Nishikawa, and A. E. Motter, Phys. Rev. E 95, 062215 (2017)], however, that in networks with asymmetrically coupled oscillators, synchronization can only be found to be stable when the oscillators are heterogenous or nonidentical. In this manuscript, it is proven, mathematically, that the conclusions in those works are incorrect, and that stable synchronization states can, and do, exist in asymmetrically coupled homogeneous oscillators. Theoretical results are confirmed with numerical simulations.

Automated summary

Synchronization among symmetrically coupled homogeneous oscillators is common, but recent studies have shown that stable synchronization in asymmetric networks can only be achieved with heterogeneous oscillators. This paper mathematically proves and numerically confirms that stable synchronization can exist in asymmetrically coupled homogeneous oscillators.