A memristive neuron with double capacitive variables coupled by Josephson junction

Continuous firing patterns in biological neurons result from time-varying electromagnetic field accompanied by energy exchange between magnetic field and electric field in the cell, which the intracellular ions are diffused and membrane channels are open for ions propagation across the outer and inner cell membranes. Incorporation of memristive terms of the neuron models can describe the effect of electromagnetic induction and even the regulation from external applied physical field. During circuit approach and implement for a neural circuit, capacitors are used to mimic the capacitive properties of the cell membrane, while inductors, nonlinear resistor and constant voltage source are effective to mimic the physical properties of ion channels. This paper proposed a neural circuit composed of two capacitors via Josephson junction connection, and the paralleled branch circuits are connected by using an inductor and a memristor. The absence using of both linear and nonlinear resistors reduces consumption of Joule heat. Energy function for the two kinds of memristive neurons are obtained and proofed, stochastic/coherence resonance is induced under noisy excitation at moderate noise intensity. Stability and bifurcation analysis clarified the main dynamical and physical property of the suggested neural circuits and their equivalent dimensionless models. Finally, an adaptive growth law is suggested to control the membrane parameter and mode transition between firing patterns is discussed in detail. That is, the neural circuit coupled with memristor and Josephson junction is effective to describe the electrical property and dynamical characteristic even without using any resistive components.