Abstract
The Hindmarsh–Rose (HR) neuron model is built to describe the neuron electrical activities. Due to the polynomial nonlinearities, multipliers are required to implement the HR neuron model in analog. In order to avoid the multipliers, this brief presents a novel smooth nonlinear fitting scheme. We first construct two nonlinear fitting functions using the composite hyperbolic tangent functions and then implement an analog multiplierless circuit for the two-dimensional (2D) and three-dimensional (3D) HR neuron models. To exhibit the nonlinear fitting effects, numerical simulations and hardware experiments for the fitted HR neuron model are provided successively. The results show that the fitted HR neuron model with analog multiplierless circuit can display different operation patterns of resting, periodic spiking, and periodic/chaotic bursting, entirely behaving like the original HR neuron model. The analog multiplierless circuit has the advantage of low implementation cost and thereby it is suitable for hardware implementation of large-scale neural networks.
Highlights
Neuron, as an essential element of neural network, can exhibit diverse electrical activities in response to the externally imposed stimuli [1,2,3]
These electronic neurons with analog and digital circuit implementations are capable to reproduce lots of different neuron dynamics and spiking/bursting behaviors that might appear in biological neurons [25, 31]
Encouraged by the above piecewise liner approximation approaches, this paper presents a novel smooth nonlinear fitting scheme to implement an analog multiplierless circuit for the 2D/3D HR neuron model
Summary
As an essential element of neural network, can exhibit diverse electrical activities in response to the externally imposed stimuli [1,2,3]. Rahimian et al implemented a two-compartmental Pinsky-Rinzel pyramidal neuron model in digital [30], Imani et al investigated the multiplierless realization of a coupled Wilson neuron model in digital [32], and Haghiri et al employed a low-cost digital design to implement the noisy Izhikevich neuron model without multipliers [33] These electronic neurons with analog and digital circuit implementations are capable to reproduce lots of different neuron dynamics and spiking/bursting behaviors that might appear in biological neurons [25, 31]. Encouraged by the above piecewise liner approximation approaches, this paper presents a novel smooth nonlinear fitting scheme to implement an analog multiplierless circuit for the 2D/3D HR neuron model.
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