Information pattern stability in memristive Izhikevich neural networks

Abstract

In this paper, modulational instability (MI) of information via membrane potential is studied analytically and numerically in an improved Izhikevich neural network under electromagnetic induction. By applying the powerful discrete multiple scale expansion method, a spatiotemporal nonlinear amplitude differential-difference equation governing the information dynamics is derived from the generic model. Linear stability of plane impulse wave solution is then performed on the latter and the impact of electromagnetic induction feedback through the memristor couplings is portrayed on the growth rate diagram. From the diagram, it is found that negative memristor coupling parameter decreases the critical amplitude while positive parameter increases the critical amplitude. To support our analytical predictions, numerical simulations are performed and data selected from the unstable zone of MI lead to the formation of localized solitonic energy patterns, related to the energy coding patterns in the nervous system. Furthermore, the sampled time series for membrane potential under the influence of memristor coupling revealed the breakdown of action potential into multiple impulse-wave trains for high parameter values thus confirming an analytical prediction. Our results provide a potential way to manipulate information coding in the brain.