Martens Erik A
Max Planck Research Group for Biological Physics and Evolutionary Dynamics, Max Planck Institute for Dynamics and Selforganization (MPIDS), Göttingen, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jul;82(1 Pt 2):016216. doi: 10.1103/PhysRevE.82.016216. Epub 2010 Jul 29.
We study a triangular network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but more weakly to those in neighboring populations than to those in their own population. This triangular network is the simplest discretization of a continuous ring of oscillators. Yet it displays an unexpectedly different behavior: in contrast to the lone stable chimera observed in continuous rings of oscillators, we find that this system exhibits two coexisting stable chimeras. Both chimeras are, as usual, born through a saddle-node bifurcation. As the coupling becomes increasingly local in nature they lose stability through a Hopf bifurcation, giving rise to breathing chimeras, which in turn get destroyed through a homoclinic bifurcation. Remarkably, one of the chimeras reemerges by a reversal of this scenario as we further increase the locality of the coupling, until it is annihilated through another saddle-node bifurcation.
我们研究了由三个具有相同频率的耦合相位振子群体组成的三角网络。这些群体进行非局部相互作用，即所有振子相互耦合，但与相邻群体中的振子的耦合比与自身群体中的振子的耦合更弱。这个三角网络是连续振子环的最简单离散化形式。然而，它表现出意想不到的不同行为：与在连续振子环中观察到的单一稳定嵌合体不同，我们发现这个系统呈现出两种共存的稳定嵌合体。像往常一样，这两种嵌合体都是通过鞍结分岔产生的。随着耦合在本质上变得越来越局部化，它们通过霍普夫分岔失去稳定性，产生呼吸嵌合体，而呼吸嵌合体又通过同宿分岔被破坏。值得注意的是，当我们进一步增加耦合的局部性时，其中一种嵌合体通过这种情况的逆转重新出现，直到它通过另一个鞍结分岔被消灭。
