Nonlinear Electronic Circuits Research Articles

Coupled Memristor Oscillators for Neuromorphic Locomotion Control: Modeling and Analysis.

The recent surge of interest in brain-inspired architectures along with the development of nonlinear dynamical electronic devices and circuits has enabled energy-efficient hardware realizations of several important neurobiological systems and features. Central pattern generator (CPG) is one such neural system underlying the control of various rhythmic motor behaviors in animals. A CPG can produce spontaneous coordinated rhythmic output signals without any feedback mechanism, ideally realizable by a system of coupled oscillators. Bio-inspired robotics aims to use this approach to control the limb movement for synchronized locomotion. Hence, devising a compact and energy-efficient hardware platform to implement neuromorphic CPGs would be of great benefit for bio-inspired robotics. In this work, we demonstrate that four capacitively coupled vanadium dioxide (VO2) memristor-based oscillators can produce spatiotemporal patterns corresponding to the primary quadruped gaits. The phase relationships underlying the gait patterns are governed by four tunable bias voltages (or four coupling strengths) making the network programmable, reducing the complex problem of gait selection and dynamic interleg coordination to the choice of four control parameters. To this end, we first introduce a dynamical model for the VO2 memristive nanodevice, then perform analytical and bifurcation analysis of a single oscillator, and finally demonstrate the dynamics of coupled oscillators through extensive numerical simulations. We also show that adopting the presented model for a VO2 memristor reveals a striking resemblance between VO2 memristor oscillators and conductance-based biological neuron models such as the Morris-Lecar (ML) model. This can inspire and guide further research on implementation of neuromorphic memristor circuits that emulate neurobiological phenomena.

Comparative Analysis of Microservice and Serverless Technology Building Automatic Design Systems for Calculating the Instability of the Static Mode of Nonlinear Electronic Circuits

Comparative Analysis of Microservice and Serverless Technology Building Automatic Design Systems for Calculating the Instability of the Static Mode of Nonlinear Electronic Circuits

Comparative Analysis of Microservice and Serverless Technology Building Automatic Design Systems for Calculating the Instability of the Static Mode of Nonlinear Electronic Circuits

Methods for constructing distributed automation systems for circuit design to calculate the instability of the coordinates of the operating points of the static mode of nonlinear electronic circuits were considered. Two-terminal networks of type R and transmission parameters of dependent sources, as well as characteristicsof external influences (temperature, radiation, etc.) are taken as components that change under the influence of external factors. To solve the problem of calculating the instability of the coordinates of the operating points of the static mode of nonlinear electronic circuits, a technique is proposed based on the use of an auxiliary circuit, which is constructed by transposing the description of the original circuit. The features of the organization of serverless and microservice architecture for building circuit design automation systems are analyzed. The multitenant design of a microservice information system environment is described. The mechanismof operation of the service as a service is presented to ensure the operation of the business logic of the server component.

Discrete-time robust event-triggered actuator fault-tolerant control based on adaptive networks and reinforcement learning

This paper focuses on the topic of fault-tolerant control for discrete-time systems with nonlinear uncertainties and actuator faults. It considers both passive and active faults as part of the analysis and design. The proposed adaptive controller, based on a nonlinear electronic circuit, handles offset-biasing, sensitivity variation, and dead-zone effects. An event-triggered mechanism, utilizing a sliding surface, enhances robustness and reduces data transmission. Adaptive networks called MiFRENs are employed, trained using reinforcement learning. Theoretical analysis guarantees boundedness of internal signals and tracking error. Experimental results validate the scheme, demonstrating required conditions, reduced data transmission, and robust performance. Comparative evaluations confirm its superiority

Noise–dissipation relation for nonlinear electronic circuits

An extension of fluctuation–dissipation theorem is used to derive a “speed limit” theorem for nonlinear electronic devices. This speed limit provides a lower bound on the dissipation that is incurred when transferring a given amount of electric charge in a certain amount of time with a certain noise level (average variance of the current). This bound, which implies a high energy dissipation for fast, low-noise operations (such as switching a bit in a digital memory), brings together recent results of stochastic thermodynamics into a form that is usable for practical nonlinear electronic circuits, as we illustrate on a switching circuit made of an nMOS pass gate in a state-of-the-art industrial technology.

Saddle-node bifurcation of periodic orbit route to hidden attractors.

Hidden attractors are present in many nonlinear dynamical systems and are not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route to these attractors is still not fully understood. In this Research Letter, we present the route to hidden attractors in systems with stable equilibrium points and in systems without any equilibrium points. We show that hidden attractors emerge as a result of the saddle-node bifurcation of stable and unstable periodic orbits. Real-time hardware experiments were performed to demonstrate the existence of hidden attractors in these systems. Despite the difficulties in identifying suitable initial conditions from the appropriate basin of attraction, we performed experiments to detect hidden attractors in nonlinear electronic circuits. Our results provide insights into the generation of hidden attractors in nonlinear dynamical systems.

Preventing Vanishing Gradient Problem of Hardware Neuromorphic System by Implementing Imidazole-Based Memristive ReLU Activation Neuron.

With advances in artificial intelligent services, brain-inspired neuromorphic systems with synaptic devices have recently attracted significant interest to circumvent the von Neumann bottleneck. However, the increasing trend of deep neural network parameters causes huge power consumption and large area overhead of a nonlinear neuron electronic circuit, and it incurs a vanishing gradient problem. Here, we present a memristor-based compact and energy-efficient neuron device to implement a rectifying linear unit (ReLU) activation function. To emulate the volatile and gradual switching of the ReLU function, we propose a copolymer memristor with a hybrid structure using a copolymer/inorganic bilayer. The functional copolymer film developed by introducing imidazole functional groups enables the formation of nanocluster-type pseudo-conductive filaments by boosting the nucleation of Cu nanoclusters, causing gradual switching. The ReLU neuron device is successfully demonstrated by integrating the memristor with an amorphous InGaZnO thin-film transistors, and achieves 0.5 pJ of energy consumption based on sub-10μA operation current and high-speed switching of 650ns. Furthermore, device-to-system-level simulation using neuron devices on the MNIST dataset demonstrates that the vanishing gradient problem is effectively resolved by five-layer deep neural networks. The proposed neuron device will enable the implementation of high-density and energy-efficient hardware neuromorphic systems. This article is protected by copyright. All rights reserved.

Accelerating DC Circuit Simulation through Feature Selection and LSTM-Based Time-Step Control

Circuit simulation has become increasingly significant in circuit design with the development of very large scale integration, and direct current (DC) analysis, which serves as the basis of circuit behavior analysis, is the foundation for nonlinear electronic circuit simulation. Among the several continuation algorithms for DC analysis, pseudo-transient analysis (PTA) methods have gained great success. However, PTA tends to be computationally intensive without a proper time-step control method. In order to improve this problem, we propose a novel time-step control method enhanced by advanced deep learning in this paper. Specifically, a coarse and fine-grained hybrid sampling strategy is introduced to find the optimal time step, which resolves the problem that the optimal time step has no precise definition in PTA theory. After that, a long short-term memory (LSTM) network, with the ability to process temporal information, can be employed to learn the optimal time-step control method based on feature selection and a two-stage data preprocessing strategy, which accelerates DC analysis. Furthermore, random forest (RF) is also used to evaluate feature importance, which can achieve feature selection with reduced dimensions, thereby speeding up the network’s training speed and improving the accuracy of prediction. Experimental results demonstrate a significant speedup: up to 61.32 times.

On a New Three-Dimensional Chaotic System with Adaptive Control and Chaos Synchronization

A three-dimensional autonomous deterministic chaotic system having six parameters is explored within this article. The dynamical characteristics of the proposed system are investigated through eigenvalues structure, bifurcation diagrams, Kaplan–Yorke dimension, Lyapunov exponents, time response, and phase plane trajectories. For the suitable design of the system parameters, it is found that the system can exhibit periodic, period-n, or chaotic oscillations. Accordingly, the system’s dynamical behavior to the variation of its coefficients has been explored. The obtained results revealed that the proposed dynamical system does not lose its chaotic oscillations for the small fluctuations of one or more of the values of its parameters. In addition, chaos control and chaos synchronization have been studied by means of the adaptive control strategy relying on Lyapunov’s second method of stability. The numerical simulation revealed that superior chaos control and master-slave synchronization have been achieved by the applied control laws. Finally, the obtained results have been simulated via a nonlinear electronic circuit that demonstrated the feasibility of the purposed chaotic system for different engineering applications such as secure communications, cryptosystems, image encryption, and image processing.

Quantiser-based Hands-off control for robust [𝒦, 𝒦ℒ] sector

This article discusses a quantiser-based stabilisation problem for uncertain nonlinear systems with the aid of robust [ K , KL ] sector. We confirmed that the quantised-feedback control steers the state trajectories of the uncertain nonlinear systems within the robust [ K , KL ] sector in finite time by adjusting the quantisation parameters. Furthermore, control-Lyapunov functions are helpful to obtain sufficient conditions for ensuring the closed-loop system's asymptotic stability and the reachability of the robust [ K , KL ] sector. Finally, a nonlinear electronic circuit is provided to test the effectiveness of the designed control law.

A Study of Chaos in Nonlinear Electronic Circuits and Applications in Game Theory

Chaos is a ubiquitous part of daily life. The weather, fractal landscapes, and the double pendulum all embody the notion of chaos. The general concepts and the key characteristics of chaos are explored and manifested in a nonlinear electronic circuit known as the Chua’s circuit. The Chua’s Circuit was built and characterized to illustrate chaos behavior in the form of Lorenz attractors. The circuit chaotic behavior was further demonstrated in a numerical model built in MATLAB. More practical chaos applications in secure communication and game theory are discussed. A case study is presented at the end to apply the chaos concept into the model of the strength of poker hands, which displays properties of a chaotic system and resembles Elementary Cellular Automata (ECA) in the chaos application.

A simple electronic circuit demonstrating Hopf bifurcation for an advanced undergraduate laboratory

A nonlinear electronic circuit comprising of three nodes with a feedback loop is analyzed. The system has two stable states, a uniform state and a sinusoidal oscillating state, and it transitions from one to another by means of a Hopf bifurcation. The stability of this system is analyzed with nonlinear equations derived from a repressilator-like transistor circuit. The apparatus is simple and inexpensive, and the experiment demonstrates aspects of nonlinear dynamical systems in an advanced undergraduate laboratory setting.

Modeling and implementation of a novel active voltage balancing circuit using deep recurrent neural network with dropout regularization

SummaryRecurrent neural networks (RNN) emerged as powerful tools to model and analyze the nonlinear behavior of electronic circuits accurately and quickly. Efforts to improve the accuracy of RNN will lead to the design of better‐quality products, which is essential in various fields such as the design of energy harvesting (EH) systems. EH techniques can provide the electrical energy needed for low‐power electronics without the need for a battery or with minimal dependency. Due to the importance of the active voltage balancing circuit in EH systems, we have proposed a new macromodeling method called dropout local‐feedback deep recurrent neural network (Dropout‐LFDRNN) to model and analyze this circuit along with two other nonlinear circuits as examples. This technique is an advance over the LFDRNN macromodeling method, and based on the obtained results from the measurements, we were able to build a fast macromodel for the active balancing circuit, which outperforms conventional deep recurrent neural network modeling method in terms of accuracy without sacrificing speed. It is worth mentioning that this proposed technique in this paper can be considered a viable approach for modeling and analysis of nonlinear electronic components and circuits. In addition to the advantage of generating a more accurate model, the model based on the Dropout‐LFDRNN approach is much faster than the existing transistor‐level models.

Large deviations theory for noisy nonlinear electronics: CMOS inverter as a case study

The latest generation of transistors are nanoscale devices whose performance and reliability are limited by thermal noise in low-power applications. Therefore developing efficient methods to compute the voltage and current fluctuations in such non-linear electronic circuits is essential. Traditional approaches commonly rely on adding Gaussian white noise to the macroscopic dynamical circuit laws, but do not capture rare fluctuations and lead to thermodynamic inconsistencies. A correct and thermodynamically consistent approach can be achieved by describing single-electron transfers as Poisson jump processes accounting for charging effects. But such descriptions can be computationally demanding. To address this issue, we consider the macroscopic limit which corresponds to scaling up the physical dimensions of the transistor and resulting in an increase of the number of electrons on the conductors. In this limit, the thermal fluctuations satisfy a Large Deviations Principle which we show is also remarkably precise in settings involving only a few tens of electrons, by comparing our results with Gillespie simulations and spectral methods. Traditional approaches are recovered by resorting to an ad hoc diffusive approximation introducing inconsistencies. To illustrate these findings, we consider a low-power CMOS inverter, or NOT gate, which is a basic primitive in electronic design. Voltage (resp. current) fluctuations are obtained analytically (semi-analytically) and reveal interesting features.

Frequency multiplication by collective nanoscale spin-wave dynamics.

Frequency multiplication is a process in modern electronics in which harmonics of the input frequency are generated in nonlinear electronic circuits. Devices based on the propagation and interaction of spin waves are a promising alternative to conventional electronics. The characteristic frequency of these excitations is in the gigahertz (GHz) range and devices are not readily interfaced with conventional electronics. Here, we locally probe the magnetic excitations in a soft magnetic material by optical methods and show that megahertz-range excitation frequencies cause switching effects on the micrometer scale, leading to phase-locked spin-wave emission in the GHz range. Indeed, the frequency multiplication process inside the magnetic medium covers six octaves and opens exciting perspectives for spintronic applications, such as all-magnetic mixers or on-chip GHz sources.

A Hybrid Approach Based on Recurrent Neural Network for Macromodeling of Nonlinear Electronic Circuits

This paper proposes a hybrid approach combining Recurrent Neural Network (RNN) and polynomial regression methods for time-domain modeling of nonlinear circuits. The proposed hybrid RNN-polynomial regression (HRPR) method merges RNN and polynomial regression which leads to a significant reduction in training time while providing speedup in simulation compared to both conventional RNN and existing models in simulation tools without sacrificing accuracy. The proposed HRPR method comprises two steps: First, an RNN structure is generated, and then, the output of the RNN is combined with external input(s) of the circuit to perform a regression. Applying this method causes part of the training process to be done by polynomial regression which is simpler than training an RNN. Also, the RNN used in the HRPR method has a simpler structure than a single conventional RNN used for modeling the same component. To verify the validity of the proposed method, modeling and comparisons of three nonlinear examples are presented in this paper.

Atomic Dynamics From Coupled Quantized Electronic Oscillators

The quantum mechanical concept of an ”atom in a molecule" is synthetically emulated and analyzed in the form of a nonlinear electronic circuit. The circuit is comprised of coupled quantized oscillators. Quantized oscillators are novel and not generally known. Such systems are shown to be consistent with quantum chemical dynamics. Such a network of quantized oscillators achieves equilibriums that are consistent with naturally occurring molecules. These capabilities offer an alternative to von Neumann digital based computations, whereby solutions to complex systems are determined as equilibriums, as is the case of nature. Historically, quantized solutions have been associated with solutions to Shrödinger’s Equation. Shrödinger Equation based observations are typically rendered, if possible, by numerical calculations. By comparison, the approach presented in this work relies on synthesizing quantized electronic devices, which are novel, in order to achieve dynamical interactions consistent with naturally occurring ones. Detailed dynamics based on actual devices are provided. The theoretical underpinnings are described. This topic has broad implications for a variety of concepts associated with quantum mechanics, including computations and entanglement, as well as various oscillator circuits of fundamental importance.

Stochastic Thermodynamics of Nonlinear Electronic Circuits: A Realistic Framework for Computing Around kT

We provide a general theory of nonlinear electronic circuits subjected to thermal noise. The devices constituting the circuit can have arbitrary I−V curves but must display shot noise. This theory includes tunnel junctions, diodes, and MOS transistors in subthreshold operation, among others. The stochastic nonequilibrium thermodynamics of these circuits is also established. The irreversible entropy production is expressed in terms of thermodynamic potentials and forces, and its fluctuations satisfy fluctuation theorems. Our theory is ideally suited to formulate a thermodynamics of computing with realistic architectures, where the reduction in transistor size and operating voltages make thermal fluctuations increasingly important. We demonstrate this point in two ways: first, by proposing a stochastic model of a CMOS inverter whose actual transfer function deviates from the deterministic one due to nonequilibrium fluctuations, and, second, by proposing a low-power full-CMOS design for a probabilistic bit (or binary stochastic neuron) exploiting intrinsic noise.8 MoreReceived 1 October 2020Revised 2 July 2021Accepted 8 July 2021DOI:https://doi.org/10.1103/PhysRevX.11.031064Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium & irreversible thermodynamicsThermodynamicsThermodynamics of computationPhysical SystemsStochastic dynamical systemsStochastic networksStatistical PhysicsNonlinear DynamicsCondensed Matter, Materials & Applied PhysicsNetworks

Chaotic dynamics in memristive circuits with different ϕ − q characteristics

SummaryThere are two ideal memristive devices, first‐order memristor and second‐order memristor, which could be widely applied in nonlinear electronic circuits. The main difference between them is their ϕ − q characteristics. However, there are only a few studies available in the literature about the different dynamic behavior that can be observed when they are connected in the same circuit in turns. In this paper, to demonstrate the different consequences for the above situation, the complex dynamics of a memristive band‐pass filter (BPF) are analyzed in detail as one of the classical first‐order circuits. Also, the existence of coexisting attractors, hysteretic dynamics, and antimonotonicity are confirmed. Subsequently, the impact of memristor coefficients on the working dynamics of BPF is revealed. The conclusion is that a higher‐order memristor can lead to a greater number of chaotic attractors and more complex nonlinearity, which is the basis to determine that substitutability and interchangeability of equivalent memristance do not apply for memristor devices with the different ϕ − q relationship when analyzing memristive circuits. Finally, the experimental simulations are presented to further prove the above theoretical analysis. Additionally, other circuits, such as the Chua circuit and the Jerk circuit, are also investigated in order to verify our analysis. In particular, a full Feigenbaum tree is demonstrated in the Chua circuit.

Physical-stochastic continuous-time identification of a forced Duffing oscillator

Despite the simplicity of the Duffing oscillator, its dynamical behaviour is extremely rich. Hence, the Duffing equations are used to describe the dynamic behaviour of many real-world nonlinear systems for a wide range of frequency bands and amplitude of the excitation signal in basic sciences and engineering. For example, the Duffing oscillator has been successfully used to model a variety of physical processes such as stiffening springs, beam buckling, nonlinear electronic circuits, superconducting Josephson parametric amplifiers, and ionisation waves in plasmas etc. Therefore, the identification of the Duffing oscillator model/parameters directly from the measured input–output data is a topic of active research in many scientific fields In this paper, we use the concept of stochastic differential equations (SDEs) to identify a model of the Duffing oscillator. SDE-based grey-box models allow us to capture the underlying mathematical structure describing the physics of the system (e.g. the original Duffing equations) using the drift term and explicitly handling of model uncertainty (or the process noise) using the diffusion term whereas the measurement uncertainty is modelled using the measurement noise term respectively. In this paper, we propose a slight variation of the maximum likelihood estimation framework used for the identification of SDEs based grey-box models yielding improved performance for long-term predictions. The proposed framework is combined with an iterative residual analysis to develop a grey-box model of the forced Duffing oscillator. The benchmark data from the so-called Brussels “Silverbox system”, which is an electrical circuit mimicking the forced Duffing oscillator dynamics is used for the identification purpose. Finally, the identified model performance (the simulation errors) is compared with the existing results available in the literature.