Pattern formation dynamics in a Memristor Cellular Nonlinear Network structure with a numerically stable VO2 memristor model

In this work, we explore pattern formation dynamics across a diffusively coupled Memristor Cellular Nonlinear Network (MCNN), which is composed of identical cells with locally active memristors. We bias the cells on the edge-of-chaos, introduce a systematic design procedure to induce complexity in the array, and extract the element values analytically in a parametric form. In order to enhance the stability and speed of the numerical simulations, we apply a simple variable transformation to a core memristor model while we include the additional effect of parasitic resistors to investigate the locally active dynamics of a VO2 device. We first take a close look at the effect of the linear coupling resistor on pattern formation, and later study how nonlinearly-resistive coupling, based upon tangent hyperbolic law, affect the emergence of complex patterns. Simulation results reveal that a variety of static patterns with different characteristics can emerge across the proposed MCNN

On Local Activity and Edge of Chaos in a NaMLab Memristor

Local activity is the capability of a system to amplify infinitesimal fluctuations in energy. Complex phenomena, including the generation of action potentials in neuronal axon membranes, may never emerge in an open system unless some of its constitutive elements operate in a locally active regime. As a result, the recent discovery of solid-state volatile memory devices, which, biased through appropriate DC sources, may enter a local activity domain, and, most importantly, the associated stable yet excitable subdomain, referred to as edge of chaos, which is where the seed of complexity is actually planted, is of great appeal to the neuromorphic engineering community. This paper applies fundamentals from the theory of local activity to an accurate model of a niobium oxide volatile resistance switching memory to derive the conditions necessary to bias the device in the local activity regime. This allows to partition the entire design parameter space into three domains, where the threshold switch is locally passive (LP), locally active but unstable, and both locally active and stable, respectively. The final part of the article is devoted to point out the extent by which the response of the volatile memristor to quasistatic excitations may differ from its dynamics under DC stress. Reporting experimental measurements, which validate the theoretical predictions, this work clearly demonstrates how invaluable is non-linear system theory for the acquirement of a comprehensive picture of the dynamics of highly non-linear devices, which is an essential prerequisite for a conscious and systematic approach to the design of robust neuromorphic electronics. Given that, as recently proved, the potassium and sodium ion channels in biological axon membranes are locally active memristors, the physical realization of novel artificial neural networks, capable to reproduce the functionalities of the human brainmore closely than state-of-the-art purely CMOS hardware architectures, should not leave aside the adoption of resistance switching memories, which, under the appropriate provision of energy, are capable to amplify the small signal, such as the niobium dioxide micro-scale device fromNaMLab, chosen as object of theoretical and experimental study in this work

A Deep Study of Resistance Switching Phenomena in TaOx ReRAM Cells: System-Theoretic Dynamic Route Map Analysis and Experimental Verification

The multidisciplinary field of memristors calls for the necessity for theoreticallyinclined researchers and experimenters to join forces, merging complementary expertise and technical know-how, to develop and implement rigorous and systematic techniques to design variability-aware memristor-based circuits and systems. The availability of a predictive physics-based model for a memristor is a necessary requirement before commencing these investigations. An interesting dynamic phenomenon, occurring ubiquitously in non-volatile memristors, is fading memory. The latter may be defined as the appearance of a unique steady-state behavior, irrespective of the choice of the initial condition from an admissible range of values, for each stimulus from a certain family, for example, the DC or the purely-AC periodic input class. This paper first provides experimental evidence for the emergence of fading memory effects in the response of a TaOx redox-based random access memory cell to inputs from both of these classes. Leveraging the predictive capability of a physics-based device model, called JART VCM v1, a thorough system-theoretic analysis, revolving around the Dynamic Route Map graphic tool, is presented. This analysis allows to gain a better understanding of the mechanisms, underlying the emergence of history erase effects, and to identify the main factors, that modulate this nonlinear phenomenon, toward future potential applications

A Compact SPICE Model for Organic TFTs and Applications to Logic Circuit Design

This work introduces a compact DC model developed for organic thin film transistors (OTFTs) and its SPICE implementation. The model relies on a modified version of the gradual channel approximation that takes into account the contact effects, occurring at nonohmic metal/organic semiconductor junctions, modeling them as reverse biased Schottky diodes. The model also comprises channel length modulation and scalability of drain current with respect to channel length. To show the suitability of the model, we used it to design an inverter and a ring oscillator circuit. Furthermore, an experimental validation of the OTFTs has been done at the level of the single device as well as with a discrete-component setup based on two OTFTs connected into an inverter configuration. The experimental tests were based on OTFTs that use small molecules in binder matrix as an active layer. The experimental data on the fabricated devices have been found in good agreement with SPICE simulation results, paving the way to the use of the model and the device for the design of OTFT-based integrated circuits.This work was supported in part by the MIUR by means of the national Program PON R&C 2007-2013 and in part by project “Elettronica su Plastica per Sistemi Smart disposable” PON02 00355 3416798

A Compact SPICE Model for Organic TFTs and Applications to Logic Circuit Design

This work introduces a compact DC model developed for organic thin film transistors (OTFTs) and its SPICE implementation. The model relies on a modified version of the gradual channel approximation that takes into account the contact effects, occurring at nonohmic metal/organic semiconductor junctions, modeling them as reverse biased Schottky diodes. The model also comprises channel length modulation and scalability of drain current with respect to channel length. To show the suitability of the model, we used it to design an inverter and a ring oscillator circuit. Furthermore, an experimental validation of the OTFTs has been done at the level of the single device as well as with a discrete-component setup based on two OTFTs connected into an inverter configuration. The experimental tests were based on OTFTs that use small molecules in binder matrix as an active layer. The experimental data on the fabricated devices have been found in good agreement with SPICE simulation results, paving the way to the use of the model and the device for the design of OTFT-based integrated circuits.This work was supported in part by the MIUR by means of the national Program PON R&C 2007-2013 and in part by project “Elettronica su Plastica per Sistemi Smart disposable” PON02 00355 3416798

Mathematical Investigation of Static Pattern Formation with a Locally Active Memristor Model

We present the mathematical investigation of static pattern formation in a Memristor Cellular Nonlinear Network (M-CNN), in consideration of the theory of local activity. The M-CNN has a planar grid form composed of identical memristive cells, which are purely resistively coupled to each other. The single cell contains a DC voltage source, a bias resistor, and a locally active memristor in parallel with a capacitor. The memristor model employed has a simple generic form which helps to reduce the simulation time, and has a functional AC equivalent circuit which facilitates further calculations. We adopt a circuit theoretical approach for the stability analysis of the single cell and a 3-cell ring configuration, as well as the examination of local activity, edge-of-chaos, and sharp-edge-of-chaos domains, which helps us to interpret the results in a better way. The emergence of static patterns is successfully confirmed by simulating the proposed resistively coupled M-CNN utilizing locally active memristors

Exact Inductorless Realization of Chua Circuit Using Two Active Elements

In this brief, we present two inductorless realizations of Chua's circuit in an exact form while using only two active elements, namely a current feedback operational amplifier (CFOA) for the precise implementation of the Chua circuit equations, and an op-amp for the realization of the active nonlinear resistor. First, we analyze the widely used Wien bridge based modified Chua circuit and apply a variable transformation and reveal the difference of its mathematical model from the original Chua circuit in a precise form. Second, we present an exact inductorless implementation of the Chua circuit employing the Wien bridge structure, using two active elements only. Third, we introduce another simple yet exact inductorless implementation of the Chua circuit with a featured property where the state variable corresponding to the inductor current of the original Chua circuit can be accessed as a capacitor voltage. Chaotic attractors obtained by experimental realizations match well with the result of numerical simulations, demonstrating the success of the proposed designs

Analytical Investigation of Pattern Formation in an M-CNN with Locally Active NbOx Memristors

This paper presents the analytical investigation of complex pattern formation in a Memristor Cellular Nonlinear Network (M-CNN) by applying the theory of local activity. The proposed M-CNN has the conventional two dimensional (2D) planar structure, where all the memristive cells are identical and resistively coupled to each other. The single cell is composed of a suitable combination of a DC voltage source, a bias resistor, a locally active NbOx memristor, and a capacitor. The locally active memristor has a simplified generic form, enhancing the simulation speed, and a functional AC equivalent circuit, facilitating further inspections. The stability analysis of the single cell is followed by the extraction of the parameters of the local activity, edge-of-chaos, and sharp-edge-of-chaos domains. Simulation results demonstrate that pattern formation can emerge in a dissipatively coupled M-CNN with locally active memristors

Exploration of Edge of Chaos in Bio-Inspired Devices, Circuits, and Systems

With Moore's era approaching an inevitable end, much research is currently focused on multi-purpose nano-devices, which may endow traditional purely-CMOS circuits with add-on functionalities, allowing to boost the performance of integrated circuits, despite further reductions in transistor dimensions shall no longer be viable. One of the most promising nanotechnologies for fostering progress in electronics in the years to come allows to fabricate memristors, which, depending upon their constitutive materials, may pave the way toward the circuit realisation of disruptive in-memory computing or mem-computing paradigms of great appeal to the Internet-of-Things industry. Moreover, with their extraordinary capability to capture the rich dynamics of neural structures, memristors shall play a key role in the development of miniaturised hardware systems operating according to principles similar to the mechanisms underlying the functionalities of the human brain. In this regard this work sheds light into the conditions, under which electronic systems, leveraging the locally-active behaviour of a NbO device stack, may enter a particular operating regime, hosting the seed for complexity, and referred to as Edge of Chaos, similarly as axon membranes on the verge to generate all-or-none spikes, which, travelling across neural structures, enable the development of intelligence in human beings