In this brief we provide a complete analytical model for the time evolution of the state of a real-world memristor under any dc stimulus and for all initial conditions. The analytical dc model is derived through the application of mathematical techniques to Strachan's accurate mathematical description of a tantalum oxide nano-device from Hewlett Packard Labs. Under positive dc inputs the state equation of the Strachan model can be solved analytically, providing a closed-form expression for the device memory state response. However, to the best of our knowledge, the analytical integration of the state equation of the Strachan model under dc inputs of negative polarity is an unsolved mathematical problem. In order to bypass this issue, the state evolution function is first expanded in a series of Lagrange polynomials, which reproduces accurately the original model predictions on the device off-switching kinetics. The solution to the resulting state equation approximation may then be computed analytically by applying methods from the field of mathematics. Our full analytical model matches both qualitatively and quantitatively the tantalum oxide memristor response captured by the original differential algebraic equation set to typical stimuli of interest such as symmetric and asymmetric pulse excitations. It is further insensitive to the convergence issues that typically arise in the numerical integration of the original model, and may be easily integrated into software programs for circuit synthesis, providing designers with a reliable tool for exploratory studies on the capability of a certain circuit topology to satisfy given design specifications.
This paper presents a fully digital implementation of a memristor hardware (HW) simulator, as the core of an emulator, based on a behavioral model of voltage-controlled threshold-type bipolar memristors. Compared to other analog solutions, the proposed digital design is compact, easily reconfigurable, demonstrates very good matching with the mathematical model on which it is based, and complies with all the required features for memristor emulators. We validated its functionality using Altera Quartus II and ModelSim tools targeting low-cost yet powerful field-programmable gate array families. We tested its suitability for complex memristive circuits as well as its synapse functioning in artificial neural networks, implementing examples of associative memory and unsupervised learning of spatiotemporal correlations in parallel input streams using a simplified spike-timing-dependent plasticity. We provide the full circuit schematics of all our digital circuit designs and comment on the required HW resources and their scaling trends, thus presenting a design framework for applications based on our HW simulator.
For the first time, the model of a physical nano-scale memristor is integrated analytically. A closed-form expression for the time evolution of the device memristance during the turn-on process is mathematically derived. The complexity of the inverse imaginary error function-based analytical formula clearly reflects the high degree of nonlinearity in the nano-device switching kinetics, which may typically span several orders of magnitude and is critically dependent on input and initial condition. The excellent agreement between the analytical solution and numerical simulation results clearly demonstrates the correctness of the theoretical derivation. The introduction of this formula represents the first step towards a systematic approach to circuit design with memristors.
Nonlinear circuits may be synchronized with interconnections that evolve in time incorporating mechanisms of adaptation found in many biological systems. Such dynamics in the links is efficiently implemented in electronic devices by using memristors. However, the approach requires a massive amount of interconnections (of the order of N2, where N is the number of nonlinear circuits to be synchronized). This issue is solved in this paper by adopting a memristor crossbar architecture for adaptive synchronization. The functionality of the structure is demonstrated, with respect to different switching characteristics, via a simulation-based evaluation using a behavioral threshold-type model of voltage-controlled bipolar memristor. In addition, we show that the architecture is robust to device variability and faults: quite surprisingly, when faults are localized, the performance of the approach may also improve as adaptation becomes more significant.
Slime mold Physarum polycephalum optimizes its foraging behaviour by minimizing the distances between the sources of nutrients it spans. When two sources of nutrients are present, the slime mold connects the sources, with its protoplasmic tubes, along the shortest path. We present a two-dimensional mesh grid memristor based model as an approach to emulate Physarum's foraging strategy, which includes space exploration and reinforcement of the optimally formed interconnection network in the presence of multiple aliment sources. The proposed algorithmic approach utilizes memristors and LC contours and is tested in two of the most popular computational challenges for Physarum, namely maze and transportation networks. Furthermore, the presented model is enriched with the notion of noise presence, which positively contributes to a collective behavior and enables us to move from deterministic to robust results. Consequently, the corresponding simulation results manage to reproduce, in a much better qualitative way, the expected transportation networks.
The ability of slime mould to learn and adapt to periodic changes in its environment inspired scientists to develop behavioral memristor-based circuit models of its memory organization. The computing abilities of slime mould Physarum polycephalum have been used in several applications, including to solve mazes. This work presents a circuit-level bio-inspired maze-solving approach via an electronic model of the oscillatory internal motion mechanism of slime mould, which emulates the local signal propagation and the expansion of its vascular network. Our implementation takes into account the inherent noise existent in the equivalent biological circuit, so that its behavior becomes closer to the non-deterministic behavior of the real organism. The efficiency and generality of the proposed electronic computing medium was validated through SPICE-level circuit simulations and compared with data from two cardinally different biological experiments, concerning 1) enhancing of Physarum's protoplasmic tubes along shortest path and 2) chemo-tactic growth by diffusing chemo-attractants.
Cellular Automata (CA) have been introduced many decades ago as one of the most efficient parallel computational models able to simulate various physical processes and systems where the interactions are local. In this paper, we are trying to advance the application of CA in modeling wildfires by accounting for the fuzziness intrinsic to the numerous environmental variables and mechanisms engaged with the emergence of the phenomenon itself. The proposed Fuzzy CA (FCA) model adopts a data-driven approach, based on evolutionary optimization, which allows incorporating knowledge from real wildfires in order to enhance its accuracy. The main difficulty for doing so arrives from the computational complexity of the proposed framework and the burden of computational resources needed for its application, which would prevent the real-time prediction of fire spread scenarios. In order to tackle the aforementioned difficulties, we propose model's fully parallel implementations in Graphical Processing Units (GPUs) and Field Programmable Gate Arrays (FPGAs) hardware. In the article, we first investigate the speedup achieved by the developed parallel implementations. Then, we present and discuss two applications to heterogeneous landscapes through comparisons with observed wildfires. Moreover, we compare the proposed framework with two different modelling approaches and results found are really promising.
Cellular Automata (CA) is a nature-inspired and widespread computational model which is based on the collective and emergent parallel computing capability of units (cells) locally interconnected in an abstract brain-like structure. Each such unit, referred as CA cell, performs simplistic computations/processes. However, a network of such identical cells can exhibit nonlinear behavior and be used to model highly complex physical phenomena and processes and to solve problems that are highly complicated for conventional computers. Brain activity has always been considered one of the most complex physical processes and its modeling is of utter importance. This work combines the CA parallel computing capability with the nonlinear dynamics of the memristor, aiming to model brain activity during the epileptic seizures caused by the spreading of pathological dynamics from focal to healthy brain regions. A CA-based confrontation extended to include long-range interactions, combined with the recent notion of memristive electronics, is thus proposed as a modern and promising parallel approach to modeling of such complex physical phenomena. Simulation results show the efficiency of the proposed design and the appropriate reproduction of the spreading of an epileptic seizure.
Unconventional computing has been studied intensively, even after the appearance of CMOS technology. Currently, it has returned to the spotlight because CMOS is about to reach its physical limits, given that the constant demand for more computational power requires for novel unconventional computing solutions. In this area, the oscillatory internal motion mechanism of slime mould, namely Physarum Polycephalum, could serve as an alternative concept for the design and development of electronic circuits that exploit the memristive dynamics and simple LC contours to deliver solutions for computationally hard to be solved problems. In this direction, this work presents how bio-inspired memristive LC oscillators with a coupling capacitor can be synchronized to perform the functionalities of a biological neuron, also able to execute more complex computations, aiming to model biological neural systems much more advanced than the neuron-less slime mould biological organism. This work proposes a connection between the function mechanism of a simple biological organism and that of complex biological systems, made in a plausible and sufficient manner, towards unconventional computation with memristors.
Memristors promise to revolutionise the world of electronics in the years to come. Besides their most popular applications in the fields of non-volatile memory design and neuro-morphic system development, their ability to process signals and store data in the same physical location may allow the conception of novel mem-computing machines outperforming state-of-the-art hardware systems suffering from the Von Neumann bottleneck. The complexity of real-world memristor models, capturing the inherent nonlinearity of the switching kinetics of the nanodevices, is one of the obstacles towards an extensive exploration of the full potential of memristors in nanoelectronics. It is well-known, in fact, that serious convergence issues frequently arise in the numerical simulation of the differential algebraic equation sets modelling the dynamics of real-world memristors. In this work we propose a strategy to develop a general closed-form mathematical representation of a real-world voltage-controlled memristor manufactured by Hewlett Packard Enterprise. The study aims to derive an analytical formula for the memductance of the nano-device under a general voltage input, starting off from the DC case. This research should be of great benefit to circuit designers, which typically use analytical formulas for the first hands-on calculations in the search for circuit topologies satisfying a certain set of specifications.
Cellular Automata (CAs) is a well-known parallel, bio-inspired, computational model. It is based on the capability of simpler, locally interacting units, i.e. the CAs cells, to evolve in time, giving rise to emergent computation, suitable to model physical system behavior, prediction of natural phenomena and multi-dimensional problem solutions. Moreover, at the same time CAs constitute a promising computing platform, beyond the von Neumann architecture. In this paper, a memristor device is considered to be the basic module of a CA cell circuit implementation, performing as a combined memory and processing element to implement CA-based circuits, able to model sufficiently systems and applications as mentioned above, targeting tentatively to a more energy efficient design compared to the conventional electronics. In particular and as a proof of concept, the results of elementary CAs modeling and simulation for the generation of pseudo-random numbers are presented using a 1-D memristor-based CAs array to illustrate the robustness and the efficacy of the proposed computing approach.
Given the complexity of the mathematical descriptions of real nanodevices with memristor fingerprints, convergence issues often emerge in the simulation of circuits employing memristors, even for a limited number of instances. Actually the simulation of one-memristor circuits may also be troublesome for some inputs and/or initial conditions. This problem prevents a thorough test of memristor circuit designs, representing a severe obstacle towards an extensive use of memristors in electronics. In this work we propose techniques to transform a highly-reliable physics-based model of the Tantalum oxide memristor from Hewlett Packard Labs in a form which lends itself naturally to stable numerical simulations. The results of this study shall pave the way towards a more extensive exploration of the full potential of memristors in integrated circuit design.
We propose the use of memristor crossbar for synchronizing nonlinear chaotic circuits. By means of this approach, the nonlinearity and memory features of the memristors are exploited to massively couple the dynamical system units with weights (the state variable of the memristors) which evolve as function of the differences between the state variables of the circuits. In this extended abstract we briefly illustrate the approach and numerical results confirming its suitability.
FPGAs are reconfigurable electronic platforms, well-suited to implement complex artificial neural networks (ANNs). To this end, the compact hardware (HW) implementation of artificial synapses is an important step to obtain human brain-like functionalities at circuit-level. In this context, the memristor has been proposed as the electronic analogue of biological synapses, but the price of commercially available samples still remains high, hence motivating the development of HW emulators. In this work we present the first digital memristor emulator based upon a voltage-controlled threshold-type bipolar memristor model. We validate its functionality in low-cost yet powerful FPGA families. We test its suitability for complex memristive circuits and prove its synaptic properties in a small associative memory via a perceptron ANN.
Within an ever-increasing variety of applications for memristors, adaptive electronic circuits have attracted considerable attention lately. This paper extends previously published work on memristive filter design to include the potential of composite memristive devices as damping elements in LC-based sensing circuits. The collective response of several LC contours with different memristive damping is considered. A thorough study of the circuit properties is performed in an attempt to exploit the high sensitivity of the circuit, other than address it as a typical drawback. The simulated circuits could find application in bio-inspired information processing, whereas could lead to better behavioral models for biological organisms.
This paper presents a Fuzzy Cellular Automata (FCA) model with the aim to cope with the computational complexity and data uncertainties that characterize the simulation of wildfire spreading on real landscapes. Moreover, parallel implementations of the proposed FCA model, on both GPU and FPGA, are discussed and investigated. According to the results, the parallel models exhibit significant speedups over the corresponding sequential algorithm. As a possible application, the proposed model could be embedded on a portable electronic system for real-time prediction of fire spread scenarios.