  In this paper, we focus on the emergence of diverse neuronal oscillations
arising in a mixed population of neurons with different excitability
properties. These properties produce mixed mode oscillations (MMOs)
characterized by the combination of large amplitudes and alternate subthreshold
or small amplitude oscillations. Considering the biophysically plausible,
Izhikevich neuron model, we demonstrate that various MMOs, including MMBOs
(mixed mode bursting oscillations) and synchronized tonic spiking appear in a
randomly connected network of neurons, where a fraction of them is in a
quiescent (silent) state and the rest in self-oscillatory (firing) states. We
show that MMOs and other patterns of neural activity depend on the number of
oscillatory neighbors of quiescent nodes and on electrical coupling strengths.
Our results are verified by constructing a reduced-order network model and
supported by systematic bifurcation diagrams as well as for a small-world
network. Our results suggest that, for weak couplings, MMOs appear due to the
de-synchronization of a large number of quiescent neurons in the networks. The
quiescent neurons together with the firing neurons produce high frequency
oscillations and bursting activity. The overarching goal is to uncover a
favorable network architecture and suitable parameter spaces where Izhikevich
model neurons generate diverse responses ranging from MMOs to tonic spiking.

Adaptation and Self-Organizing Systems;Chaotic Dynamics;Biological Physics