Dynamics of a nonlinear resistor-coupled memristive neuron with double membrane

The neuronal cell membrane has a bilayer structure, where the flexible material shows nonlinearity and can be simulated by a nonlinear resistor. The inner and outer membranes are modeled by two capacitors. In this paper, a nonlinear resistor connected with two capacitors simulates a nonlinear cell membrane. Based on the property of the magnetic flux-controlled memristor to perceive external magnetic fields, a novel functional double membrane neuron model with a nonlinear membrane is obtained. The dynamic equations of this neuronal circuit are established based on Kirchhoff's law, and the Hamilton energy function of the neuron is formulated following Helmholtz's theorem. The dynamics dependent on initial states are investigated, and the behavior of the functional neuron is explored both in the absence of external interference and under different magnetic field stimuli by using time sampling sequences, phase diagrams, Lyapunov exponents, and bifurcation diagrams. Furthermore, the energy distribution and self-regulatory capacity of the double membrane neuron under magnetic fields are also analyzed. The results demonstrate that complex firing patterns (spiking and chaotic) can be elicited in the double membrane neuron by adjusting the initial values of variables, circuit parameters, and magnetic field signals. These observed complex dynamics reflect the sensitivity of the model to external stimuli. This work offers novel insights and methodologies for neural network design and application.