Numerical approach and physical description for a two-capacitive neuron and its adaptive network dynamics

A simple neuron containing one capacitive variable can mimic the dynamical property of electrical activities in a biological neuron. Functional enhancement and activation of adaptive regulation must clarify the energy characteristic and nonlinear property of cell membrane of the neuron. In this work, two capacitors are connected via a nonlinear resistor for exploring the electrical activities in a double-layer nonlinear membrane, and the additive branch circuits are incorporated with piezoelectric ceramic and Josephson junction, which can perceive external acoustic wave and changes of magnetic field. The nonlinear equations for the neural circuit are converted into equivalent dimensionless neuron model in the form of nonlinear oscillator. The energy function for the neuron model is defined and proofed by using the Helmholtz theorem. Any mode transition is dependent on the shift of energy levels and coherence resonance is induced by noisy excitation. An adaptive control law under energy flow is proposed to regulate the firing patterns. Finally, the neuron is clustered to build a neural network with nearest neighbor coupling on a square array. Statistical synchronization factor is defined and calculated to predict the synchronization stability and wave propagation in the neural network. By activating the adaptive growth of coupling intensity and capacitance ratio for the outer and inner cell membrane, target like waves are developed in the neural network.