Memristor Circuits for Simulating Neuron Spiking and Burst Phenomena.

Giacomo Innocenti,Mauro Di Marco,Mauro Forti,Alberto Tesi

doi:10.3389/fnins.2021.681035

Giacomo Innocenti, Mauro Di Marco + Show 2 more

Open Access

https://doi.org/10.3389/fnins.2021.681035

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Abstract

Since the introduction of memristors, it has been widely recognized that they can be successfully employed as synapses in neuromorphic circuits. This paper focuses on showing that memristor circuits can be also used for mimicking some features of the dynamics exhibited by neurons in response to an external stimulus. The proposed approach relies on exploiting multistability of memristor circuits, i.e., the coexistence of infinitely many attractors, and employing a suitable pulse-programmed input for switching among the different attractors. Specifically, it is first shown that a circuit composed of a resistor, an inductor, a capacitor and an ideal charge-controlled memristor displays infinitely many stable equilibrium points and limit cycles, each one pertaining to a planar invariant manifold. Moreover, each limit cycle is approximated via a first-order periodic approximation analytically obtained via the Describing Function (DF) method, a well-known technique in the Harmonic Balance (HB) context. Then, it is shown that the memristor charge is capable to mimic some simplified models of the neuron response when an external independent pulse-programmed current source is introduced in the circuit. The memristor charge behavior is generated via the concatenation of convergent and oscillatory behaviors which are obtained by switching between equilibrium points and limit cycles via a properly designed pulse timing of the current source. The design procedure takes also into account some relationships between the pulse features and the circuit parameters which are derived exploiting the analytic approximation of the limit cycles obtained via the DF method.

Highlights

The ever-growing need of computing power to handle data intensive applications is seriously challenging conventional digital von Neumann computing architectures (Bonomi et al, 2012; Satyanarayanan, 2017; Williams, 2017)
A memristor circuit composed of a resistor, an inductor, a capacitor, an ideal charge-controlled memristor and an independent current source as input is considered
A first-order periodic approximation is obtained in an analytic way for each limit cycle via the Describing

Summary

INTRODUCTION

The ever-growing need of computing power to handle data intensive applications is seriously challenging conventional digital von Neumann computing architectures (Bonomi et al, 2012; Satyanarayanan, 2017; Williams, 2017). The physical separation between the computing and memory units can generate long latency time and large energy consumption when data intensive tasks are performed. In this context, researchers look at the emerging nanoscale analog devices, such as memristors, as a viable approach for developing new computing paradigms, based on in-memory and analog computation, which are potentially capable to overcome the limitations of conventional computer architectures (Waldrop, 2016; Zidan et al, 2018; Krestinskaya et al, 2020)

A Memristor Circuit for Spiking and Bursting

PROBLEM FORMULATION AND PRELIMINARIES

A Memristor Circuit for Spiking and Bursting B

INPUT-LESS MEMRISTOR CIRCUIT DYNAMICS

Equilibrium Points

Limit Cycles

MODELING NEURON DYNAMICS VIA THE CONTROLLED CIRCUIT

CONCLUSIONS