A bimembrane neuron for computational neuroscience

A biological neuron has endomembrane and extracellular membrane, and its capacitive effect can be described in an equiavlent neural circuit composed of two capacitors. In this paper, a smooth nonlinear resistor with cubic term for the current-voltage (i-v) is introduced into a nonlinear circuit connected with two capacitors and one inductor. The characteristic of field energy is analyzed and unknown parameters are identified with adaptive law. Furthermore, a magnetic flux-controlled memristor (MFCM) is connected to this circuit to estimate its memristive effect on dynamics and energy flow. After scale transformation, the two kinds of nonlinear circuits are replaced by equivalent neuron models, which can present similar spiking, bursting patterns as those presented in biological neurons. Energy function is obtained in theoretical way for discerning the relation between mode selection and energy level. Noisy disturbance is applied to induce coherence resonance, and the involvement of memristive current can induce coherence resonance with lower noise intensity. The results confirmed that energy flow can be controlled to regulate the electric activities in neurons, and higher energy level is obtained in periodic patterns of neuron under coherence resonance. This neural circuit and the memristive model are more suitable for identifying the neural activities in nervous system composed of biological neurons.