{"title":"Modelling of memristor networks and the effective memristor","authors":"","doi":"10.1016/j.automatica.2024.111922","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0005109824004163/pdfft?md5=5954be949d5faa6ab8a4d214958bffed&pid=1-s2.0-S0005109824004163-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109824004163","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
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.
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.
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