Periodic two-cluster synchronization modes in fully coupled networks of nonlinear oscillators

We consider special systems of ordinary differential equations, the so-called fully coupled networks of nonlinear oscillators. For a given class of systems, we propose methods that allow examining problems of the existence and stability of periodic two-cluster synchronization modes. For any of these modes, the set of oscillators falls into two disjoint classes. Within these classes, complete synchronization of oscillations is observed, and every two oscillators from different classes oscillate asynchronously.