This book introduces the basic fundamentals, models, emulators and analyses of mem-elements in the circuit theory with applications. The book starts reviewing the literature on mem-elements, models and their recent applications. It presents mathematical models, numerical results, circuit simulations, and experimental results for double-loop hysteresis behavior of mem-elements. The authors introduce a generalized memristor model in the fractional-order domain under different input and different designs for emulator-based mem-elements, with circuit and experimental results. The basic concept of memristive-based relaxation-oscillators in the circuit theory is also covered. The reader will moreover find in this book information on memristor-based multi-level digital circuits, memristor-based multi-level multiplier and memcapacitor-based oscillators and synaptic circuits.
Studies in Systems, Decision and Control 26 Ahmed G. Radwan Mohammed E. Fouda On the Mathematical Modeling of Memristor, Memcapacitor, and Meminductor Studies in Systems, Decision and Control Volume 26 Series editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland e-mail:
[email protected] About this Series The series “Studies in Systems, Decision and Control” (SSDC) covers both new developments and advances, as well as the state of the art, in the various areas of broadly perceived systems, decision making and control- quickly, up to date and with a high quality. The intent is to cover the theory, applications, and perspectives on the state of the art and future developments relevant to systems, decision making, control, complex processes and related areas, as embedded in the fields of engineering, computer science, physics, economics, social and life sciences, as well as the paradigms and methodologies behind them. The series contains monographs, textbooks, lecture notes and edited volumes in systems, decision making and control spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output. More information about this series at http://www.springer.com/series/13304 Ahmed G. Radwan Mohammed E. Fouda • On the Mathematical Modeling of Memristor, Memcapacitor, and Meminductor 123 Ahmed G. Radwan Faculty of Engineering, Engineering Mathematics and Physics Department Cairo University Giza Egypt Mohammed E. Fouda Faculty of Engineering, Engineering Mathematics and Physics Department Cairo University Giza Egypt and Nanoelectronics Integrated Systems Center (NISC) Nile University Cairo Egypt ISSN 2198-4182 ISSN 2198-4190 (electronic) Studies in Systems, Decision and Control ISBN 978-3-319-17490-7 ISBN 978-3-319-17491-4 (eBook) DOI 10.1007/978-3-319-17491-4 Library of Congress Control Number: 2015937018 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissi