Implementation of the Hindmarsh–Rose Model Using Stochastic Computing

Oscar Camps, Stavros G. Stavrinides, Carol de Benito and Rodrigo Picos ()
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Oscar Camps: Industrial Engineering and Construction Department, University of Balearic Islands, 07122 Palma, Spain
Stavros G. Stavrinides: Physics Department, International Hellenic University, 65404 Kavala, Greece
Carol de Benito: Industrial Engineering and Construction Department, University of Balearic Islands, 07122 Palma, Spain
Rodrigo Picos: Industrial Engineering and Construction Department, University of Balearic Islands, 07122 Palma, Spain

Mathematics, 2022, vol. 10, issue 23, 1-11

Abstract: The Hindmarsh–Rose model is one of the most used models to reproduce spiking behaviour in biological neurons. However, since it is defined as a system of three coupled differential equations, its implementation can be burdensome and impractical for a large number of elements. In this paper, we present a successful implementation of this model within a stochastic computing environment. The merits of the proposed approach are design simplicity, due to stochastic computing, and the ease of implementation. Simulation results demonstrated that the approximation achieved is equivalent to introducing a noise source into the original model, in order to reproduce the actual observed behaviour of the biological systems. A study for the level of noise introduced, according to the number of bits in the stochastic sequence, has been performed. Additionally, we demonstrate that such an approach, even though it is noisy, reproduces the behaviour of biological systems, which are intrinsically noisy. It is also demonstrated that using some 18–19 bits are enough to provide a speedup of x2 compared to biological systems, with a very small number of gates, thus paving the road for the in silico implementation of large neuron networks.

Keywords: stochastic logic; chaotic systems; approximate computing; Hindmarsh–Rose system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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