Palacios Antonio
Nonlinear Dynamical Systems Group, Department of Mathematics, San Diego State University, San Diego, California 92182, USA.
Phys Rev E. 2021 Feb;103(2-1):022206. doi: 10.1103/PhysRevE.103.022206.
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)PRLTAO0031-900710.1103/PhysRevLett.117.114101 and Y. Zhang, T. Nishikawa, and A. E. Motter, Phys. Rev. E 95, 062215 (2017)2470-004510.1103/PhysRevE.95.062215], 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.
耦合振子之间的同步是具有均匀（即相同）振子的对称耦合网络的一个常见特征。然而，最近有报道称 [T. 西川和A. 莫特，《物理评论快报》117, 114101 (2016)PRLTAO0031 - 900710.1103/PhysRevLett.117.114101以及Y. 张、T. 西川和A. E. 莫特，《物理评论E》95, 062215 (2017)2470 - 004510.1103/PhysRevE.95.062215]，在具有非对称耦合振子的网络中，只有当振子是异质的或不相同的时候，同步才能被发现是稳定的。在本论文中，通过数学证明，那些论文中的结论是不正确的，并且在非对称耦合的均匀振子中确实存在稳定的同步状态。理论结果通过数值模拟得到了证实。
