Discrete hybrid Izhikevich neuron model: nodal and network behaviours considering electromagnetic flux coupling

Abstract

We analyse the dynamics of the improved discretised version of the well known Izhikevich neuron model under the action of external electromagnetic field. It is found that the three-dimensional IZH map shows rich dynamics. With the variation of the electromagnetic field, period-doubling route to chaos in a repeating fashion is observed from the bifurcation diagram. Even the forward and backward 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 networks 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.