Guest Editorial: Memristive electronic circuits, neural networks and neuromorphic computing

© 2024 The Author(s). Electronics Letters published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology. This is an open access article under the Creative Commons Attribution Non-Commercial No-Derivatives CC BY-NC-ND licence, https://creativecommons.org/licenses/by-nc-nd/4.0/The theoretical concept of memristor was first proposed as the fourth basic circuit element by Chua in 1971. It defines the relationship between electric charge and magnetic flux. The first physical implementation of memristor was realised by HP Labs in 2008. It was fabricated in advanced nano technology. Intensive research has since been conducted on the development of memristors across the whole world and wide applications of memristors have also been explored. Since they are smaller nano device, consume less power, and have both memory and processing functions, memristors have been widely recognised to be the future of electronics, computing and AI. For example, they will play a key role in emerging edge computing and brain-like computing. The aim of the Special Issue is to follow the state of the arts of memristor-based circuits and systems, with particular focus on memristive electronic circuits, neural networks and neuromorphic computing, publish original technical papers reflecting the most recent research and application results, and identify new challenges and ways forward for future research and applications in this emerging fast-growing field.Peer reviewe

High Frequency Response of Volatile Memristors

In this theoretical study, we focus on the high-frequency response of the electrothermal NbO2-Mott threshold switch, a real-world electronic device, which has been proved to be relevant in several applications and is classified as a volatile memristor. Memristors of this kind, have been shown to exhibit distinctive non-linear behaviors crucial for cutting-edge neuromorphic circuits. In accordance with well-established models for these devices, their resistances depend on their body temperatures, which evolve over time following Newton's Law of Cooling. Here, we demonstrate that HP's NbO2-Mott memristor can manifest up to three distinct steady-state oscillatory behaviors under a suitable high-frequency periodic voltage input, showcasing increased versatility despite its volatile nature. Additionally, when subjected to a high-frequency periodic voltage signal, the device body temperature oscillates with a negligible peak-to-peak amplitude. Since, the temperature remains almost constant over an input cycle, the devices under study behave as linear resistors during each input cycle. Based on these insights, this paper presents analytical equations characterizing the response of the NbO2-Mott memristor to high-frequency voltage inputs, demarcating regions in the state space where distinct initial conditions lead to various asymptotic oscillatory behaviors. Importantly, the mathematical methods introduced in this manuscript are applicable to any volatile electrothermal resistive switch. Additionally, this paper presents analytical equations that accurately reproduce the temperature time-waveform of the studied device during both its transient and steady-state phases when subjected to a zero-mean sinusoidal voltage input oscillating in the high-frequency limit

Real time hybrid medical image encryption algorithm combining memristor-based chaos with DNA coding

Image encryption is a commonly used method to secure medical data on a public network, playing a crucial role in the healthcare industry. Because of their complex dynamics, memristors are often used in developing novel chaotic systems that can improve the efficiency of encryption algorithms based on chaos. In this work, we propose a novel locally active memristor-based chaotic circuit model and present a real time hybrid image encryption application developed on a PYNQ-Z1 (Python Productivity for Zynq) low-cost FPGA board using Jupiter programming environment. The proposed hybrid algorithm combines memristor-based chaos with a DNA (deoxyribonucleic acid) encryption algorithm exploiting diffusion-confusion technique. We initially present a new compact and inductorless chaotic circuit, derive the model equations, and then verify its chaotic dynamics numerically through the investigation of the phase portraits, Lyapunov exponents and the bifurcation diagrams. We further implement the chaotic circuit experimentally with discrete elements. The randomness of the chaotic sequence is improved using Trivium and von Neumann post-processor algorithms and assessed through the NIST tests. Finally, the performance of the encryption algorithm is evaluated through various metrics, including histogram and correlation analyses, differential attack, information entropy, as well as data-loss and noise attack, demonstrating its security and suitability for real-time encryption systems

Pattern Formation in a RD-MCNN with Locally Active Memristors

This chapter presents the mathematical investigation of the emergence of static patterns in a Reaction–Diffusion Memristor Cellular Nonlinear Network (RD-MCNN) structure via the application of the theory of local activity. The proposed RD-MCNN has a planar grid structure, which consists of identical memristive cells, and the couplings are established in a purely resistive fashion. The single cell has a compact design being composed of a locally active memristor in parallel with a capacitor, besides the bias circuitry, namely a DC voltage source and its series resistor. We first introduce the mathematical model of the locally active memristor and then study the main characteristics of its AC equivalent circuit. Later on, we perform a stability analysis to obtain the stability criteria for the single cell. Consequently, we apply the theory of local activity to extract the parameter space associated with locally active, edge-of-chaos, and sharp-edge-of-chaos domains, performing all the necessary calculations parametrically. The corresponding parameter space domains are represented in terms of intrinsic cell characteristics such as the DC operating point, the capacitance, and the coupling resistance. Finally, we simulate the proposed RD-MCNN structure where we demonstrate the emergence of pattern formation for various values of the design parameters

Edge of Chaos Theory Unveils the First and Simplest Ever Reported Hodgkin–Huxley Neuristor

The Hodgkin-Huxley model is an accurate yet convoluted mathematical description of the complex nonlinear dynamics of a biological neuronal axon. Employing four degrees of freedom, three of which embodied by the sodium and potassium memristive ion channels, it is capable to capture the cascade of three fundamental bifurcations, specifically a Hopf supercritical, a Hopf subcritical, and a saddle-node limit cycle bifurcation, marking the life cycle from birth to extinction via All-to-None effect of an electrical spike, also referred to as Action Potential in the literature, across biological axon membranes under monotonic change in the net synaptic current. This paper recurs to powerful concepts from the Local Activity and Edge of Chaos Principle and to methods from Circuit Theory and Nonlinear Dynamics to design the first and simplest ever-reported electrical circuit, which, leveraging the peculiar Negative Differential Resistance effects in a volatile NbOx threshold switch from NaMLab, and including additionally just one capacitor and one DC current source in its minimal topology, undergoes the three-bifurcation cascade, emerging across the fourth-order Hodgkin-Huxley neuron model under monotonic current sweep, while requiring half the number of degrees of freedom, which reveals the promising potential of Memristors on “Edge of Chaos” for energy-efficient bio-inspired electronics

Whole-body tissue stabilization and selective extractions via tissue-hydrogel hybrids for high-resolution intact circuit mapping and phenotyping

To facilitate fine-scale phenotyping of whole specimens, we describe here a set of tissue fixation-embedding, detergent-clearing and staining protocols that can be used to transform excised organs and whole organisms into optically transparent samples within 1–2 weeks without compromising their cellular architecture or endogenous fluorescence. PACT (passive CLARITY technique) and PARS (perfusion-assisted agent release in situ) use tissue-hydrogel hybrids to stabilize tissue biomolecules during selective lipid extraction, resulting in enhanced clearing efficiency and sample integrity. Furthermore, the macromolecule permeability of PACT- and PARS-processed tissue hybrids supports the diffusion of immunolabels throughout intact tissue, whereas RIMS (refractive index matching solution) grants high-resolution imaging at depth by further reducing light scattering in cleared and uncleared samples alike. These methods are adaptable to difficult-to-image tissues, such as bone (PACT-deCAL), and to magnified single-cell visualization (ePACT). Together, these protocols and solutions enable phenotyping of subcellular components and tracing cellular connectivity in intact biological networks

Memristor models in chaotic neural circuits

The peculiar features of the memristor, a fundamental passive two-terminal element characterized by a nonlinear relationship between charge and flux, promise to revolutionize integrated circuit design in the next few decades. Besides its most popular potential application, ultra-dense nonvolatile memories, much research has been lately devoted to their use in chaotic neural networks for the emulation of brain activity. In the studies on neuromorphic circuits, it is common to characterize each memristor with a theoretical model based upon a single-valued odd-symmetric charge-flux nonlinearity. Memristive nano-films exhibit different dynamics depending on the way they behave at boundaries. We recently developed a mathematical model, applicable to memristive nano-structures of various nature, offering the opportunity to tune the boundary conditions so as to capture a wide gamut of distinct nonlinear behaviors. However, in general the proposed model exhibits a multivalued charge-flux nonlinearity dependent on input and initial state condition. In this paper, we first derive the necessary and sufficient set of boundary conditions under which single-valuedness is observed in this nonlinearity for any input/state initial condition combination. Then, after proving that, under such boundary conditions, the asymmetrical nonlinearities of memristors with opposite orientation are the odd-symmetric function of the other, we devise a pair of suitable memristor arrangements with odd-symmetric charge-flux characteristics. This analysis is confirmed by showing how a chaotic neural circuit employing one of such arrangements behaves similarly to its counterpart with the theoretically-modeled memristor. </jats:p