Complex mixed-mode oscillations in oscillators sharing nonlinearity

Mixed-mode oscillations (MMOs) are a typical manifestation of slow-fast dynamical systems that contains a sequence of large amplitude excursions interspersed with small amplitude oscillations. We identified complex forms of MMOs in a system of three coupled non-autonomous LCR oscillators sharing a common nonlinearity. Different sequences of MMOs and related dynamics like MMO incrementing bifurcations, Farey sequences, and amplitude-modulated spiking have been witnessed in the model as a consequence of 2-slow and 1-fast external driving frequencies. For particular parametric space, the period adding sequence of MMOs is found to follow a devil’s staircase structure. The transition between states is found to occur via torus canards explosion. We validate our observations through numerical investigation.