A neuron with asymmetric memristive channels and nonlinear membrane

Memristor-based branch circuits can present and estimate distinct field effect and then external physical field can be detected by monitoring the channel currents. The intracellular and extracellular ions have different passing probabilities across the cell membrane and thus appropriate gradient concentration is maintained to support suitable membrane potential and firing patterns under external stimulus. Therefore, it is worthy of presenting a reliable neuron model for discerning the permeability diversity of ions by connecting two different kinds of memristive channels, one controls the outer membrane while another controls the inner membrane, and the physical property of the media between inner and outer membrane is considered. In our study, two capacitors are connected via a nonlinear resistor, and two different memristors are used in the branch circuits for estimating the electrical activities during energy exchange. A two-capacitive neuron model with asymmetric memristive channels is obtained, and the energy characteristic is discussed after exact definition of the energy function. Noisy disturbance is applied for mimicking stochastic electromagnetic radiation on the neuron, and coherence resonance is detected and predicted by calculating the distribution of average energy with noise intensity in the neuron. Finally, field coupling via charge exchanges is activated to reveal the self-organization and pattern formation in the neural network, and the spatial patterns are controlled by the adaptive growth of membrane capacitance ratio for outer and inner membranes. Our suggested neuron model contains two memristive channels and double capacitive variables, and it is more suitable to match the physical property of biological neurons in presence of external electromagnetic field.