  We analyse the dynamics of the improved discretised version of the well known
Izhikevich neuronmodel under the action of external electromagnetic field. It
is found that the three-dimensional IZHmap shows rich dynamics. With the
variation of the electromagnetic field, period-doubling routeto chaos in a
repeating fashion is observed from the bifurcation diagram. Even the forward
andbackward continuation bifurcation diagram which do not completely overlap
suggests that there is multistability in the system. The phenomenon of
bistability (coexistence of periodic and chaotic attractors) is observed. The
presence of periodic and chaotic attractor is aided by the maximal Lyapunov
exponent diagram. The Lyapunov phase diagram of electromagnetic field and
synapses current shows a large parameter region of chaotic and periodic
behaviors with the presence of unbounded regions as well. The IZH map shows a
plethora of spiking and bursting patterns such as mixed-mode patterns, tonic
spiking, phasic spiking, steady spikes, regular spikes, spike bursting,
periodic bursting, phasic bursting, chaotic firing, etc with the variation of
electromagnetic coupling strength and the synapses current. We also investigate
the presence of chimera states in a ring-star, ring, star network of IZH map
neurons. Chimera states are found in the case of ring-star and ring network
while synchronised clusters were found in the case of star network and are
aided by the spatiotemporal plots, space-time plot, recurrence plots. The rich
dynamics shown by the discretised IZH map makes it a promising research model
to study about neurodynamics.
