  The desynchronization problems in oscillatory networks is considered. A new
desynchronization notion is introduced and desynchronization conditions are
provided. The desynchronization notion is formulated in terms of Yakubovich
oscillatority of the auxiliary synchronization error system. As an example, the
network of diffusively coupled FitzHugh-Nagumo systems with undirected graph is
considered. The simple inequality guaranteeing network desynchronization is
derived. The simulation results confirm the validity of the obtained analytical
results.
