Complete dynamical analysis of a neuron under magnetic flow effect

In the last decades, many studies have been done about nervous system from the mathematical and computational point of view. Many mathematical models have been proposed to describe neuron. Most of them have described the membrane potential of a neuron in terms of the leakage current and the synaptic inputs. Very recently, according to the Maxwell electromagnetic induction theorem, researchers proposed a new neuron model which considers inner magnetic fluctuation and external electromagnetic radiation as a significant missing part that can participate in neural activity. In this paper, dynamical properties of this new model, such as equilibria and its stability, phase portraits, bifurcation diagram, Lyapunov exponents, and basin of attraction, are investigated. Moreover, an implementation of electronic circuit and FPGA is also done to verify the feasibility of the theoretical model.