Modelling of memristor networks and the effective memristor

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-09-21 DOI:10.1016/j.automatica.2024.111922

Anne-Men Huijzer, Arjan van der Schaft, Bart Besselink

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Abstract

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.

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忆阻器网络建模和有效忆阻器

本文提出了忆阻器网络建模和分析的数学框架，我们将忆阻器描述为电荷和磁通量之间的单调关系。利用这一框架，我们证明单调忆阻器网络的端口行为可以等同于用一个单调忆阻器（即所谓的有效忆阻器）来描述。有效忆阻器的行为受单个忆阻器的单调性以及忆阻器网络结构的影响。本文提供了一种算法，可以推导出任何忆阻器网络的有效忆阻器的明确特征。此外，还根据相关电阻网络的有效电阻推导出有效忆阻器曲线的明确界限。最后，还得出了串联和并联互连端口行为的明确描述，并提供了两个简单电路的仿真示例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.