Memcapacitor and Meminductor Circuit Emulators: A Review

This research was funded by the Japanese KAKENHI through Grant Number JP18k04275 and Spanish Ministry of Education, Culture, and Sport (MECD), through Project TEC2017-89955-P and Grant Numbers: FPU16/01451 and FPU16/04043.In 1971, Prof. L. Chua theoretically introduced a new circuit element, which exhibited a different behavior from that displayed by any of the three known passive elements: the resistor, the capacitor or the inductor. This element was called memristor, since its behavior corresponded to a resistor with memory. Four decades later, the concept of mem-elements was extended to the other two circuit elements by the definition of the constitutive equations of both memcapacitors and meminductors. Since then, the non-linear and non-volatile properties of these devices have attracted the interest of many researches trying to develop a wide range of applications. However, the lack of solid-state implementations of memcapacitors and meminductors make it necessary to rely on circuit emulators for the use and investigation of these elements in practical implementations. On this basis, this review gathers the current main alternatives presented in the literature for the emulation of both memcapacitors and meminductors. Different circuit emulators have been thoroughly analyzed and compared in detail, providing a wide range of approaches that could be considered for the implementation of these devices in future designs.Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (KAKENHI) JP18k04275Spanish Ministry of Education, Culture, and Sport (MECD) TEC2017-89955-P FPU16/01451 FPU16/0404

Modeling of Coupled Memristive-Based Architectures Applicable to Neural Network Models

This chapter explores the dynamic behavior of dual flux coupled memristor circuits in order to explore the uncharted territory of the fundamental theory of memristor circuits. Neuromorphic computing anticipates highly dense systems of memristive networks, and with nanoscale devices within such close proximity to one another, it is anticipated that flux and charge coupling between adjacent memristors will have a bearing upon their operation. Using the constitutive relations of memristors, various cases of flux coupling are mathematically modeled. This involves analyzing two memristors connected in composite, both serially and in parallel in various polarity configurations. The new behavior of two coupled memristors is characterized based on memristive state equations, and memductance variation represented in terms of voltage, current, charge and flux. The rigorous mathematical analysis based on the fundamental circuit equations of ideal memristors affirms the memristor closure theorem, where coupled memristor circuits behave as different types of memristors with higher complexity