Modelling of memristor networks and the effective memristor

This paper presents a mathematical framework for the modelling and analysis of networks of memristors, where we describe a memristor as a monotone relation between electric charge and magnetic flux. Using this framework, we show that the port behaviour of networks of monotone memristors can equivale...

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Bibliographic Details
Published in:	Automatica (Oxford) Vol. 171; p. 111922
Main Authors:	Huijzer, Anne-Men, van der Schaft, Arjan, Besselink, Bart
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.01.2025
Subjects:	Application of nonlinear analysis and design Memristors Neuromorphic computing Non-linear electrical circuits Memristors Non-linear electrical circuits Application of nonlinear analysis and design Neuromorphic computing
ISSN:	0005-1098
Online Access:	Get full text
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Summary:	This paper presents a mathematical framework for the modelling and analysis of networks of memristors, where we describe a memristor as a monotone relation between electric charge and magnetic flux. Using this framework, we show that the port behaviour of networks of monotone memristors can equivalently be described by a single monotone memristor, the so-called effective memristor. The behaviour of the effective memristor is influenced by the monotonicity properties of the single memristors and the structure of the network of memristors. An algorithm is provided to derive an explicit characterisation of the effective memristor of any network of memristors. In addition, explicit bounds on the effective memristance curve are derived in terms of the effective resistance of associated resistor networks. Finally, an explicit description of the port behaviour of series and parallel interconnections is derived and simulation examples are provided for two simple circuits.
ISSN:	0005-1098
DOI:	10.1016/j.automatica.2024.111922