  In this manuscript, a silent resonator neuron is coupled with a spiking
integrator neuron through the gap junction, when the coupled neurons are of
different types of excitability and none of the coupled neurons exhibit mixed
mode oscillations and bursting oscillations intrinsically. By using dynamical
systems theory (e.g. the bifurcation theory), all the observed oscillation
patterns and the transition mechanisms between them are investigated, when one
of the coupling strengths is fixed and the other is varied. It is noticeable
that, there is an interval in the parameter space, for the parameter values
within which the coupled system is multi-stable. This multistability
corresponds to the coexistence of mixed mode oscillations, bursting
oscillations and subthreshold oscillations of the resonator neuron. In
addition, some interval in the parameter space is introduced such that, for the
values of the coupling strength within which the resonator neuron is in tonic
spiking mode, while for the values of the coupling strength outside which the
resonator neuron exhibits subthreshold oscillations. It is also verified that
the final synchronization of the coupled neurons actually corresponds to the
synchronization of tonic spiking oscillations of the integrator neuron and
one-bursting oscillations of the resonator neuron.
