Physical approach of a neuron model with memristive membranes

The membrane potential of a neuron is mainly controlled by the gradient distribution of electromagnetic field and concentration diversity between intracellular and extracellular ions. Without considering the thickness and material property, the electric characteristic of cell membrane is described by a capacitive variable and output voltage in an equivalent neural circuit. The flexible property of cell membrane enables controllability of endomembrane and outer membrane, and the capacitive properties and gradient field can be approached by double membranes connected by a memristor in an equivalent neural circuit. In this work, two capacitors connected by a memristor are used to mimic the physical property of two-layer membranes, and an inductive channel is added to the neural circuit. A biophysical neuron is obtained and the energy characteristic, dynamics, self-adaption is discussed, respectively. Coherence resonance and mode selection in adaptive way are detected under noisy excitation. The distribution of average energy function is effective to predict the appearance of coherence resonance. An adaptive law is proposed to control the capacitive parameters, and the controllability of cell membrane under external stimulus can be explained in theoretical way. The neuron with memristive membranes explains the self-adaptive mechanism of parameter changes and mode transition from energy viewpoint.