Continuous energy exchange between magnetic fields supporting memristive neuron firing

Biological neurons can be excited to maintain certain firing patterns following different external stimuli, and similar changes in electrical activities can be reproduced in some neural circuits by applying an external voltage. Generic neural circuits are composed of capacitors, induction coils, resistors, and nonlinear resistors, and continuous energy exchange between the capacitive and inductive components is crucial for preserving output voltages. Incorporating nonlinear elements causes interactions between the charge flow across the capacitor and the induced electromotive force on the inductor. It is a challenge to explore the occurrence of nonlinear oscillation and coherence resonance in a neural circuit without using a capacitor and nonlinear resistor, and it considers the case lack of electric field energy. In this paper, a simple neural circuit is proposed that combines two inductors, one magnetic flux-controlled memristor (MFCM), and three resistors, with two constant voltage sources in the branch circuits used as reverse potentials in the ion channels. The field energy has an exact form, and it is stored in the circuit components as a magnetic field. Scale transformation is applied on the circuit equations and field energy function to obtain equivalent dimensionless forms of the memristive neuron and Hamilton energy. The reference values for the physical time and capacitance are represented by an appropriate combination of resistance and inductance, because the capacitance value is unavailable. The memristive neuron without capacitive effect still shows similar firing patterns, and coherence resonance is induced under noisy excitation. The emergence of coherence resonance can be predicted by calculating the distribution of the average energy <H> versus noise intensity, and the value for <H> reaches a maximum under coherence resonance. Finally, an adaptive law for parameter growth under energy control is proposed to control mode transitions in the electrical activity. The methodology and results of this work offer insights into the oscillatory mechanism of neural circuits, and showcase how magnetic field control can be used to manage neural activations.