We study the emergent dynamics of a mixed Kuramoto ensemble in the presence of both attractive and repulsive coupling strengths. To be precise, we consider coupled Kuramoto-type systems consisting of two ensembles in which the oscillators in the same group interact attractively with a positive intra-group coupling strength, whereas the oscillators in the different group communicate repulsively with a negative inter-group coupling strength. For the modeling perspective of the Kuramoto model (KM for brevity), two types of systems are treated in this paper: an attractive–repulsive inertial KM–KM and an attractive–repulsive KM–KM. For these two models, we provide sufficient frameworks leading to complete bi-polar synchronization in which asymptotic configuration tends to a bi-polar state. Our estimates mainly rely on the gradient-like flow formulation and the energy estimate.

我们研究了在有吸引力和排斥耦合强度的存在下混合仓本合奏的新兴动力。确切地说，我们考虑由两个集合组成的耦合的仓本型系统，其中同一组中的振荡器以正的组内耦合强度进行有吸引力的交互，而不同组中的振荡器以负的组间耦合进行排斥性通信。力量。从仓本模型（为简洁起见，KM）的建模角度来看，本文讨论了两种类型的系统：吸引力-排斥惯性KM-KM和吸引力-排斥惯性KM-KM。对于这两个模型，我们提供了足够的框架来导致完整的双极同步，其中渐近配置趋于双极状态。