Wave pattern stability of neurons coupled by memristive electromagnetic induction

Abstract

During the propagation of action potential, large extracellular potential as well as the difference in the transmembrane potential between adjacent nerve fibers can induce electromagnetic induction current in the neighboring fibers. This can modify the electrical and excitation behaviors of neighboring nerve fibers resulting in interneuronal communication. In this paper, the FitzHugh–Nagumo model is used to describe the local kinetics of the neuronal network and the memristive electromagnetic induction current is included to approach coupling between adjacent nerve fibers. Modulational instability technique is explored both analytically and numerically to bring out some communication features based on nonlinear structures. Through multiple scale expansion in the discrete approximation limit, we show that the dynamics of the network is governed by a well-known differential-difference nonlinear equation. The stability of the plane wave solution revealed the contribution of memristive electromagnetic induction coupling K in enhancing interneuronal communication. By exploring the long time evolution of the modulated plane wave via numerical experiments using parameters chosen from the unstable parameter region, the initiation and dynamics of the nonlinear structures agree with the analytical predictions. Extensive numerical experiments revealed the possibility of achieving perfect interneuronal communication using a controlled pitch of magnetic radiation. The results can provide guidance in developing therapy for brain seizure.