Memristors, Higher-Order Elements, and Generalized Mem-Systems: Background of the Art of Their Modeling, Simulation and Emulation

Professor Dalibor Biolek
Dept. of Electrical Engineering/Microelectronics
University of Defence/Brno University of Technology
Brno, Czech Republic
E-mail: dalibor.biolek@unob.cz
 

Abstract: The fabrication of the memristive system, denoted �TiO2 memristor�, in 2008 by Hewlett-Packard laboratories, triggered an increase of interest in this device, which was theoretically postulated as the fourth fundamental passive electrical element by L. Chua in 1971. When professor Chua called for developing other electrical components, namely memcapacitors and meminductors, at the First Symposium on Memristor and Memristive systems in 2008, he initiated a wave of discussions about which components actually belonged to the set of fundamental electrical elements, and even whether the memristor could be considered the fourth fundamental element. Although these questions continue to be discussed even today, the answers have been known since 1980, when the so-called �higher-order elements� (HOEs) or �(a, b) elements� were introduced into the circuit theory. The HOEs brought a certain framework and order into the circuit theory, underlying the fact that the long-established triad of fundamental electrical elements � R, C, and L � are merely a fragment of a much more complicated reality, which can be described by Chua�s table of HOEs. In addition to the concept of fundamental circuit elements, the memristors, memcapacitors, and meminductors being a well-known subset of memory elements from HOEs, also the more general memristive, memcapacitive, and meminductive systems are intensively studied due to the fact that they can model more truly the behavior of today perspective physical mechanisms of nonvolatile memories for future computer industry, artificial intelligence, and bio-inspired nanoelectronics, such as RRAM (Resistive Random Access Memory), PCM (Phase Change Memory), etc.
This tutorial discusses three possible stages of studying the memristors and related mem-systems: the creation of a model, the simulation of the behavior of an element by way of using the model and the software tools, and the hardware emulation.
The main purpose of such tools consists in their utilization in investigating theoretic circuit properties of HOEs and devices built from them, and to reveal other characteristic fingerprints of HOEs, the pinched hysteretic loop of the memristor being the most widely known. The behavioral models based on unambiguous constitutive relations or on parameter vs. state maps of the memory elements will be discussed in detail, including the way they are implemented in software tools for a fast interactive analysis. The term �interactive� denotes the instantaneous response of the simulator to the user�s modification of an arbitrary parameter of the device model. In such a way, the simulation is getting closer to the real �try and watch� laboratory experiments. The other modeling approach is also demonstrated, starting from the mutator strategy. Since mutators provide fundamentally exact copying of the shapes of constitution relations from the original to the transformed elements, an arbitrary HOE can be modeled, based for example, on the mere knowledge of the constitutive relation of nonlinear resistor.
The latter method can be used for a block-oriented concept of the emulation of memory elements and arbitrary elements from Chua's table, utilizing mutators with unified internal structures. In combination with the possibility of cascade connection of the mutators, it provides for the emulation of an arbitrary element from the table.
In addition to the above objectives, this tutorial brings an alternative view to the memory elements from the perspective of other domains than electrical engineering. Using the concept of the effort and flow, it will be shown, for example, that there are also mechanical versions of memristors, memcapacitors, and meminductors, and that this concept penetrates more branches of science.

Short biography: Dalibor Biolek received the M.Sc. degree in Electrical Engineering from Brno University of Technology, Czech Republic, in 1983, and the PhD. degree in Electronics from the Military Academy Brno, Czech Republic, in 1989, focusing on algorithms of the symbolic and numerical computer analyses of electronic circuits with a view to the linear continuous-time and switched filters.
He is currently with the Department of EE, University of Defence Brno (UDB), and with the Department of Microelectronics, Brno University of Technology (BUT), Czech Republic. His scientific activity is directed to the areas of general circuit theory, frequency filters, mem-systems, and computer simulation of electronic systems. He has published over 400 papers and is author of several books on circuit analysis and simulation. At present, he is professor at BUT and UDB in the field of Theoretical Electrical Engineering.
Prof. Biolek is a member of the CAS/COM Czech National Group of IEEE. He also serves as an Area Editor of the International Journal of Electronics and Communications (AEU).