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.