A memristive neuron with nonlinear membranes and network patterns

Abstract

Memristor-coupled nonlinear circuits can be controlled to present similar firing patterns as biological neurons, and the memristive term and magnetic flux variable in neuron models can address the effect of electromagnetic induction during neural activities. A single capacitive variable rarely discerns the material properties of the cell membrane and the field difference between the two sides of the cell membrane. In this work, a pair of capacitors is connected via a nonlinear resistor, in parallel with a magnetic flux-controlled memristor (MFCM) in an additive branch circuit, and external illumination is captured by a phototube to build a new neural circuit. The obtained memristive neuron has two capacitive variables and exact energy definition, and the double-layer cell membrane is considered as a nonlinear membrane because its dependence on channel current and potential diversity for outer and inner membranes is nonlinear form. The photocurrent controls the firing patterns and modes of electrical activities completely during energy changes, and a similar stochastic resonance is detected by measuring the distribution of the CV (coefficient of variability) and the average energy value of the neuron vs. noise intensity. When energy function is available, an adaptive growth law is proposed to control the membrane capacitance ratio and then mode transition and energy shift are regulated effectively. Finally, memristive neurons are clustered to explore the collective electrical activities by measuring pattern formation in the neural network on a square array. When the adaptive control law is activated for the coupling intensity and intrinsic bifurcation parameter,a stable target wave is induced to control the network dynamics.