Dynamical effects of memristive electromagnetic induction on a 2D Wilson neuron model.

Electromagnetic induction plays a crucial impact on the firing activity of biological neurons, since it exists along with the mutual effect between membrane potential and ions transport. Flux-controlled memristor is an available candidate in characterizing the electromagnetic induction effect. Different from the previously reported literature, a non-ideal flux-controlled memristor with cosine mem-conductance function is employed to determine the periodic magnetization and leakage flux processes in neurons. Thereafter, a three-dimensional (3D) memristive Wilson (m-Wilson) neuron model is constructed under the consideration of this kind of electromagnetic induction. Numerical simulations are performed by multiple numerical tools, which demonstrate that the 3D m-Wilson neuron model can generate abundant firing activities. Interestingly, coexisting firing activities, antimonotonicity, and firing frequency regulation are discovered under special parameter settings. Furthermore, a PCB-based analog circuit is designed and hardware measurements are executed to verify the numerical simulations. These explorations in numerical and hardware surveys might provide insights to regulate the firing activities by appropriate electromagnetic induction.

Three-dimensional memristive Morris-Lecar model with magnetic induction effects and its FPGA implementation.

To characterize the magnetic induction flow induced by neuron membrane potential, a three-dimensional (3D) memristive Morris-Lecar (ML) neuron model is proposed in this paper. It is achieved using a memristor induction current to replace the slow modulation current in the existing 3D ML neuron model with fast-slow structure. The magnetic induction effects on firing activities are explained by the spiking/bursting firings with period-adding bifurcation and periodic/chaotic spiking-bursting patterns, and the bifurcation mechanisms of the bursting patterns are elaborated using the fast-slow analysis method to create two bifurcation sets. In particular, the 3D memristive ML model can also exhibit the homogeneous coexisting bursting patterns when switching the memristor initial states, which are effectively illustrated by the theoretical analysis and numerical simulations. Finally, a digitally FPGA-based hardware platform is developed for the 3D memristive ML model and the experimentally measured results well verify the numerical ones.