Highlights• The analysis of oscillatory behavior in a coupled nonlinear system is considered• The change of coupling term and external input results in a transition to different dynamical states• The first (discontinuous) and second (continuous) phase transitions result from relaxing the mean-field assumption• Delta waves can be generated by altering inputs in a network of Jansen-Rit neural mass models, which has not been previously observed in a single Jansen-Rit neural mass analysis