Dynamical analysis of an improved FitzHugh-Nagumo neuron model with multiplier-free implementation

The cubic-polynomial nonlinearity with N-shaped curve plays a crucial role in generating abundant electrical activities for the original FitzHugh-Nagumo (FHN) neuron model. The pioneer FHN neuron model is efficient in theoretical analysis and numerical simulation for these abundant electrical activities, but analog multipliers are indispensable in hardware implementation since the involvement of cubic-polynomial nonlinearity. Analog multiplier goes against the circuit integration of FHN neuron model due to its huge implementation costs. To avoid the involvement of analog multiplier in hardware implementation, a nonlinear function possessing N-shaped curve and multiplier-free implementation is presented in this paper. To confirm the availability of this nonlinear function in generating electrical activities, numerical simulations and hardware experiments are successfully executed on an improved two-dimensional (2D) FHN neuron model with externally applied stimulus. The results demonstrate that the improved FHN neuron model can generate rich electrical activities of periodic spiking behavior, chaotic behavior, and quasi-periodic behavior. Analog circuit implementation without any multiplier and its hardware experiment show the availability of the proposed nonlinear function, which is appropriate for analog circuit implementation of FHN neuron-based neuromorphic intelligence.