  We present a study on the emergence of a variety of spatio temporal patterns
among neurons that are connected in a multiplex framework, with neurons on two
layers with different functional couplings. With the Hindmarsh-Rose model for
the dynamics of single neurons, we analyze the possible patterns of dynamics in
each layer separately and report emergent patterns of activity like in-phase
synchronized oscillations and amplitude death for excitatory coupling and
anti-phase mixed-mode oscillations in multi-clusters with phase regularities
when the connections are inhibitory. When they are multiplexed, with neurons of
one layer coupled with excitatory synaptic coupling and neurons of the other
layer coupled with inhibitory synaptic coupling, we observe transfer or
selection of interesting patterns of collective behavior between the layers.
While the revival of oscillations occurs in the layer with excitatory coupling,
the transition from anti-phase to in-phase and vice versa is observed in the
other layer with inhibitory synaptic coupling. We also discuss how theselection
of these spatio temporal patterns can be controlled by tuning the intralayer or
interlayer coupling strengths or increasing the range of non-local coupling.
With one layer having electrical coupling while the other synaptic coupling of
excitatory(inhibitory)type, we find in-phase(antiphase) synchronized patterns
of activity among neurons in both layers.
