Memristor reduces conduction failure of action potentials along axon with Hopf bifurcation

Memristor has been identified to modulate electronic activities of the nervous system, and conduction failure of action potentials along axon has been identified to play important roles in information transition related to pathological pain. In the present paper, the influences of the memristor on the conduction failure induced by the external stimulation with high frequency are investigated. After introducing electromagnetic induction mediated by memristor into Hodgkin-Hexley (HH) model, the Hopf bifurcation advances with increasing depolarization current, and the membrane potential of the resting state near the bifurcation increases. Such two changes mainly lead to the decrease of conduction failure rate of action potentials along axon which is described with a network model composed of HH neurons. Moreover, the reduction of conduction failure rate induced by memristor is well interpreted with the nonlinear dynamics near the bifurcation point, for example, the dynamics of the current threshold to evoke the second action potential from the after-potential following the first one. The results present that memristor can promote the conduction ability of action potentials along axon, which presents a novel function of memristor and contributes to the information transmission related to pathological pain in the nervous system.