Modulated wave pattern stability in chain neural networks under high–low frequency magnetic radiation

Abstract

The dynamics of localized modulated action potential induced through modulational instability (MI) in a diffusive array of coupled neurons under high–low frequency magnetic radiation is investigated both analytically and numerically in the frame work of the improved Integrate and Fire model. The improved model includes the magnetic flux variable which takes into account the effect of electromagnetic induction set up from the variation in intracellular distribution of ions concentration during action potential propagation. The coupling between the magnetic flux variable and the membrane potential variable is realized using the memristor. High–low frequency magnetic radiation is imposed as periodic forcing currents on the magnetic flux variable. Through the powerful discrete multiple scale expansion, the nonlinear system of coupled equations are simplified to a lone nonlinear amplitude differential equation, on which linear stability analysis is carried out. It is found that high memristive coupling stabilizes the growth rate of instability. The stable and unstable zones of MI portrait are clearly dependent on the memristive coupling. Numerical experiment is performed and it confirms data picked from the unstable zone lead to the formation of localized modulated wave patterns with some traits of synchronization. Extensive numerical simulations revealed higher memristive coupling suppresses the excitability of the lattice to quiescent state, with homogeneous spatiotemporal patterns. The sample time series of the membrane potential showed high–low frequency magnetic radiation factor (N) promotes mode transition from spiking to bursting-like state. This could provide new insights to develop a new therapy in controlling abnormal brain state using magnetic radiation.