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For modeling of complex systems, in signal processing, and the explorations of nonlinear dynamics and memory effects, the utilization of noninteger-order dynamics provides adaptable control over oscillation patterns and frequencies. Moreover, various waveforms result in unique sonic qualities. By manipulation of these waveforms, musicians and sound designers have the capacity to craft a wide spectrum of auditory experiences, ranging from basic tones to intricate sound scape. This paper is about study of such vibrating systems using the noninteger-order derivative operator approach. In particular, we will discuss fractional relaxation oscillator and Scott-Blair oscillator employing constant proportional Caputo fractional derivative operator. Laplace transform method and Tzou’s numerical inversion algorithm are utilized to solve these vibrating models with respective initial conditions. A thorough graphical analysis is done to discuss the control of noninteger-order parameters and the parameters involved in the definition of fractional derivative operator. Finally, useful conclusions are recorded to highlight the behavior of oscillators and influence of noninteger-order parameters, the parameters involved in the definition of fractional derivative operator and system parameters that are helpful in controlling over oscillation pattern, frequencies and shape of vibrations produced by the vibrating systems. [ABSTRACT FROM AUTHOR]

This paper presents a novel compact and shadow resistance‐to‐frequency converter and resistance‐to‐time converter. The design incorporates three current feedback operational amplifiers (CFOA) and can be implemented in CMOS technology. The design's functionality has been proven through simulation and experimental verification. The simulation and experimental findings show that the proposed design works well with small deviation between simulation and experimental results. [ABSTRACT FROM AUTHOR]

With remarkable electrical and optical switching properties induced at low power and near room temperature (68 °C), vanadium dioxide (VO2) has sparked rising interest in unconventional computing among the phase-change materials research community. The scalability and the potential to compute beyond the von Neumann model make VO2 especially appealing for implementation in oscillating neural networks for artificial intelligence applications, to solve constraint satisfaction problems, and for pattern recognition. Its integration into large networks of oscillators on a Silicon platform still poses challenges associated with the stabilization in the correct oxidation state and the ability to fabricate a structure with predictable electrical behavior showing very low variability. In this work, the role played by the different annealing parameters applied by three methods (slow thermal annealing, flash annealing, and rapid thermal annealing), following the vanadium oxide atomic layer deposition, on the formation of VO2 grains is studied and an optimal substrate stack configuration that minimizes variability between devices is proposed. Material and electrical characterizations are performed on the different films and a step-by-step recipe to build reproducible VO2-based oscillators is presented, which is argued to be made possible thanks to the introduction of a hafnium oxide (HfO2) layer between the silicon substrate and the vanadium oxide layer. Up to seven nearly identical VO2-based devices are contacted simultaneously to create a network of oscillators, paving the way for large-scale implementation of VO2 oscillating neural networks. [ABSTRACT FROM AUTHOR]

Starting from [J.-M. Ginoux et al., Torus breakdown in a uni junction memristor, Int. J. Bifurcation Chaos 28(10) (2018) 1850128; J.-M. Ginoux et al., Torus breakdown in a two-stroke relaxation memristor, Chaos Solitons Fractals 153 (2021) 111594], we define a model which describes the dynamical behavior of a class of two-stroke oscillators (i.e., nonlinear oscillators with two distinct phases per cycle). We highlight some properties of the model still not taken into account, like presence of a global bifurcation and bistability for some regions of the parameters space. We then extend the model to study two coupled two-stroke oscillators, where synchrony and anti-synchrony regimes appear as well as transient chaos and intermittency phenomena. We finally compare the theoretical results on synchrony regimes with the corresponding experimental data obtained from a circuit where two relaxation oscillators, based on the Unijunction Transistor (UJT) electronic component, are coupled together. The comparison shows a good qualitative agreement between the experiments and the theoretical results. [ABSTRACT FROM AUTHOR]

Non-normalizable states are difficult to interpret in the orthodox quantum formalism but often occur as solutions to physical constraints in quantum gravity. We argue that pilot-wave theory gives a straightforward physical interpretation of non-normalizable quantum states, as the theory requires only a normalized density of configurations to generate statistical predictions. In order to better understand such states, we conduct the first study of non-normalizable solutions of the harmonic oscillator from a pilot-wave perspective. We show that, contrary to intuitions from orthodox quantum mechanics, the non-normalizable eigenstates and their superpositions are bound states in the sense that the velocity field v y → 0 at large ± y . We argue that defining a physically meaningful equilibrium density for such states requires a new notion of equilibrium, named pilot-wave equilibrium, which is a generalisation of the notion of quantum equilibrium. We define a new H-function H pw , and prove that a density in pilot-wave equilibrium minimises H pw , is equivariant, and remains in equilibrium with time. We prove an H-theorem for the coarse-grained H pw , under assumptions similar to those for relaxation to quantum equilibrium. We give an explanation of the emergence of quantization in pilot-wave theory in terms of instability of non-normalizable states due to perturbations and environmental interactions. Lastly, we discuss applications in quantum field theory and quantum gravity, and implications for pilot-wave theory and quantum foundations in general. [ABSTRACT FROM AUTHOR]

Dependences of the components of the complex dielectric permittivity and specific electrical conductivity in the frequency range 10−2–107 Hz at temperatures of 213–433 K of guaiacol, a model compound of lignin, one of the most common biopolymers, are analyzed. Three groups of relaxation oscillators are identified. Their characteristics (relaxation time and activation energy) are determined. The activation energy is shown to change depending on the aggregate state. The results indicate that the dielectric relaxation and conductivity of lignin polymer and its model compounds are similar in an alternating electric field. [ABSTRACT FROM AUTHOR]

Sleep timing varies between individuals and can be altered in mental and physical health conditions. Sleep and circadian sleep phenotypes, including circadian rhythm sleep-wake disorders, may be driven by endogenous physiological processes, exogeneous environmental light exposure along with social constraints and behavioural factors. Identifying the relative contributions of these driving factors to different phenotypes is essential for the design of personalised interventions. The timing of the human sleep-wake cycle has been modelled as an interaction of a relaxation oscillator (the sleep homeostat), a stable limit cycle oscillator with a near 24-hour period (the circadian process), man-made light exposure and the natural light-dark cycle generated by the Earth's rotation. However, these models have rarely been used to quantitatively describe sleep at the individual level. Here, we present a new Homeostatic-Circadian-Light model (HCL) which is simpler, more transparent and more computationally efficient than other available models and is designed to run using longitudinal sleep and light exposure data from wearable sensors. We carry out a systematic sensitivity analysis for all model parameters and discuss parameter identifiability. We demonstrate that individual sleep phenotypes in each of 34 older participants (65-83y) can be described by feeding individual participant light exposure patterns into the model and fitting two parameters that capture individual average sleep duration and timing. The fitted parameters describe endogenous drivers of sleep phenotypes. We then quantify exogenous drivers using a novel metric which encodes the circadian phase dependence of the response to light. Combining endogenous and exogeneous drivers better explains individual mean mid-sleep (adjusted R-squared 0.64) than either driver on its own (adjusted R-squared 0.08 and 0.17 respectively). Critically, our model and analysis highlights that different people exhibiting the same sleep phenotype may have different driving factors and opens the door to personalised interventions to regularize sleep-wake timing that are readily implementable with current digital health technology. Author summary: Disrupted sleep has long term health consequences and affects our day-to-day ability to function physically, mentally and emotionally. But what determines when and how long we sleep? It is well-known that daily light exposure patterns determine the timing of the body clock. However, creating mathematical models that can take realistic light exposure patterns and predict plausible sleep timing has been challenging. Furthermore, nearly all previous studies have focused on developing models for average behaviour, yet sleep timing and duration are highly individual. In this paper, we present a simple model that combines sleep regulatory and circadian processes. The model can take individual light exposure patterns and, by fitting physiologically plausible parameters, describe individual mean sleep timing and duration. We test our model on data collected from 34 older participants. Our modelling approach suggests that some of the participants slept late because of physiological factors, while for other individuals, late sleep was a consequence of their light environment. This approach of combining a model with longitudinal data could be implemented in digital health technology such that your smart watch could tell you not only how you slept last night, but also how to change your light environment to sleep better tomorrow. [ABSTRACT FROM AUTHOR]

This paper proposes a temperature sensor based on temperature-frequency conversion using 180 nm CMOS technology. The temperature sensor consists of a proportional-to-absolute temperature (PTAT) current generating circuit, a relaxation oscillator with oscillation frequency proportional to temperature (OSC-PTAT), a relaxation oscillator with oscillation frequency independent of temperature (OSC-CON), and a divider circuit cascaded with D flip-flops. Using BJT as the temperature sensing module, the sensor has the advantages of high accuracy and high resolution. An oscillator that uses PTAT current to charge and discharge capacitors to achieve oscillation, and utilizes voltage average feedback (VAF) to enhance the frequency stability of the oscillator is tested. Through the dual temperature sensing process with the same structure, the influence of variables such as power supply voltage, device, and process deviation can be reduced to a certain extent. The temperature sensor in this paper was implemented and tested with a temperature measurement range of 0–100 °C, an inaccuracy of +0.65 °C/−0.49 °C after two-point calibration, a resolution of 0.003 °C, a resolution Figure of Merit (FOM) of 6.7 pJ/K2, an area of 0.059 mm2, and a power consumption of 32.9 μW. [ABSTRACT FROM AUTHOR]

In this paper, a CMOS relaxation oscillator with trimming and temperature compensation is presented for the on-chip multi-sensor systems which need MHz level frequency source. The proposed scheme uses a single current branch to charge the capacitor to generate the oscillation with voltage average feedback (VAF) circuit. Binary-weight current trimming array is adopted to reduce the frequency variation caused by the process variation under different process corners. A compensation calibration resistor array with Kelvin connection is utilized to improve the frequency variation with temperature. With the help of VAF, the frequency spread caused by the comparator delay is suppressed. This relaxation oscillator with a typical frequency of 13.4 MHz is implemented in a standard 180 nm CMOS process. Simulation results show that it achieves a frequency temperature coefficient of 28.3 ppm/∘C from − 4 0 ∘ C to 125∘C and a 0.074%/0.1 V frequency variation when supply voltage changes from 2.9 to 3.7 V. [ABSTRACT FROM AUTHOR]

This work demonstrates oscillation frequency modulation in a NbO2-based relaxation oscillator device, in which the oscillation frequency increases with operating temperature and source voltage, and decreases with load resistance. An annealing-induced oxygen diffusion at 373 K was carried out to optimize the stoichiometry of the bulk NbO2 to achieve consistent oscillation frequency shift with device temperature. The device exhibits stable self-sustained oscillation in which the frequency can be modulated between 2 and 33 MHz, and a wider operating voltage range can be obtained. An additional surface treatment step was employed during fabrication to reduce the surface roughness of the bottom electrode and to remove surface contaminants that affect the interfacial properties of the device. The device frequency tunability coupled with high oscillating frequency and high endurance capability of more than 1.5 × 108 cycles indicates that the Pt/NbO2/Pt device is particularly suitable for applications in an oscillatory neural network. [ABSTRACT FROM AUTHOR]

Electrochemical supercapacitors, one of the storage devices, have attracted much attention owing to their high power density, fast charge-discharge and long cycle life. In this study, we present findings of a hybrid system comprised of gold and polyaniline, fabricated via an in-situ , one pot synthesis route and designed for use in symmetric supercapacitor applications. The gold-polyaniline (Au-PANI) based hybrid material was thoroughly characterized using microscopic, optical, and surface analytical techniques to gain a comprehensive understanding of the system. The electrochemical performance of Au-PANI based electrode was examined using cyclic voltammetry (CV), galvanostatic charge-discharge (GCD) and electrochemical impedance spectroscopy (EIS) techniques. The hybrid system exhibited maximum specific capacitance (C S) 387 F/g at the current density of 12 A/g for three electrode system. The symmetric supercapacitor exhibited a maximum specific capacity (Q S) 303 mAh/g at the current density of 0.1 A/g and achieved a maximum energy density (ED) and power density (PD) of 243 mWh/kg and 619 W/kg at the current density of 0.1 A/g and 0.9 A/g, respectively. Further, the Au-PANI based symmetric device was applied to generate low-frequency waveforms. [Display omitted] • An in-situ , one pot synthesis route is reported for the fabrication of Au-PANI hybrid system. • Au-PANI based hybrid system was applied for supercapacitor application. • The symmetric supercapacitor exhibited specific capacity value of 303 mAh/g at the current density of 0.1 A/g. • The fabricated symmetric device was applied to generate low-frequency waveforms. [ABSTRACT FROM AUTHOR]

A frequency-modulated ultrawideband (FM-UWB) hybrid transceiver, with a high system reuse ratio up to 90%, is fabricated in the 65-nm CMOS process for both short-range wireless communication and high-resolution radar ranging. The radio frequency (RF) front-ends (RFFEs) based on module stacking and current reuse achieve significant RF power savings of about 30% and 50% for the transmitter and the receiver (RX), respectively. The presented IF zero-crossing delay discrimination benefits a high radar resolution less than 1 cm. A multimode relaxation oscillator (OSC) for the reconfigured triangular subcarrier generation and a dual-path ring voltage-controlled oscillator (VCO) for the linear FM, stacked by a wideband push–pull power amplifier (PA), generate an FCC-compliant UWB signal. An active balun embedded low-noise amplifier (LNA) and two symmetric-detuning band-passed filters (BPFs) are stacked with the bandwidth extension to linearly demodulate the UWB FM signal. Experimental results show that the 3.75–4.25-GHz hybrid transceiver has an energy efficiency of 1.9 nJ/bit with an active area of 0.7 mm2 and a power dissipation of 1.9 mW and achieves the RX sensitivity of −71 dBm and the transmitted power of −14.1 dBm, with a bit error rate (BER) of 10−4 at a distance of 4 m under the data rate (DR) of 0.1–1.0 Mbps. The transceiver also achieves the noise figure (NF) of 4.8 dB and the phase noise of −78.6 dBc/Hz at 1-MHz offset frequency. [ABSTRACT FROM AUTHOR]

The work endeavors to realize a single Voltage Differencing Current Conveyor (VDCC)-based current-controlled memristor emulator with charge-dependent linear memristance function. Such current-controlled memristors closely model the current (i)–voltage (v) relationship of the popular TiO2-based physical memristor architecture constructed by Hewlett–Packard (HP). The presented emulator circuit comprises only two grounded passive elements and two external MOS transistors along with a VDCC active element and provides the facility of electronic/resistive tunability. It is found through the detailed literature survey that the presented circuit is the most compact design to realize a charge-controlled memristance simulator as compared to any previously reported structure. The designed configuration has been verified through presented simulation results generated using PSPICE based on 0.18 μ m CMOS technology. It has also been validated through relaxation and chaotic oscillators developed using the proposed VDCC-based memristor emulator and output waveforms have been shown. Furthermore, the discussed memristor emulator has been implemented and verified through commercial ICs, AD844 and LM13700. [ABSTRACT FROM AUTHOR]

In the beginning of the Second World War, the French physicist, Yves Rocard, published a book entitled Théorie des Oscillateurs (Theory of Oscillators). In Chapter V, he designed a mathematical model consisting of a set of three nonlinear differential equations and allowing to account for economic cycles. Numerical integration of his model has highlighted a chaotic attractor. Its analysis with classical tools such as bifurcation diagram and Lyapunov Characteristic Exponents has confirmed the chaotic features of its solution. It follows that Rocard's 1941 chaotic econometric model has thus most likely preceded Lorenz' butterfly of twenty-two years. Moreover, apart from this historical discovery which upsets historiography, it is also established that this "new old" three-dimensional autonomous dynamical system is a new jerk system whose solution exhibits a chaotic attractor the topology of which varies, from a double scroll attractor to a Möbius-strip and then to a toroidal attractor, according to the values of a control parameter. [ABSTRACT FROM AUTHOR]

The phenomenon of the metal–insulator phase transition in polycrystalline vanadium dioxide (VO2) films gave rise to a new class of nonlinear dynamical systems that have found application in neuromorphic electronics. In this article, we propose the model of VO2 relaxation oscillator in the fast-slow systems’ approximation with considering thermal processes accompanying the resistivity switching at the metal–insulator transition (MIT). The differential equations describing the oscillator were reduced to dimensionless form. By means of numerical simulations, the nonlinear system was established to exhibit four types of dynamics depending on the applied electric voltage and the small parameter value of the system. The possible phase space trajectories for the dynamical system were considered for all types of dynamics, with the bursting oscillations predicted not having been observed experimentally so far. The results of this work can be applied to the neuromorphic computer operation analysis with VO2-oscillator dynamics that mimics the neural activity. [ABSTRACT FROM AUTHOR]

Coupled electronic oscillators have recently been explored as a compact, integrated circuit- and room temperature operation-compatible hardware platform to design Ising machines. However, such implementations presently require the injection of an externally generated second-harmonic signal to impose the phase bipartition among the oscillators. In this work, we experimentally demonstrate a new electronic autaptic oscillator (EAO) that uses engineered feedback to eliminate the need for the generation and injection of the external second harmonic signal to minimize the Ising Hamiltonian. Unlike conventional relaxation oscillators that typically decay with a single time constant, the feedback in the EAO is engineered to generate two decay time constants which effectively helps generate the second harmonic signal internally. Using this oscillator design, we show experimentally, that a system of capacitively coupled EAOs exhibits the desired bipartition in the oscillator phases without the need for any external second harmonic injection, and subsequently, demonstrate its application in solving the computationally hard Maximum Cut (MaxCut) problem. Our work not only establishes a new oscillator design aligned to the needs of the oscillator Ising machine but also advances the efforts to creating application specific analog computing platforms. [ABSTRACT FROM AUTHOR]

We investigate the synchronizing properties of two synaptically coupled model neurons in the presence of conduction delays. The neurons are modeled as relaxation oscillators, and they interact through inhibitory synapses that activate rapidly but decay slowly. We derive a reduced system through a slow/fast decomposition process, and special coordinates are introduced into the system. Then we construct a map, for which a stable fixed point corresponds to a stable synchronized periodic (SP) solution. The functional benefit of these coordinates is that, on the stability of an SP solution, the map can be decomposed into one-dimensional submaps. By analyzing these submaps, we examine how conduction delays affect the stability of the SP solution, depending on the period and duty cycle of an intrinsic oscillator and the synaptic decay rate. [ABSTRACT FROM AUTHOR]

Neural circuits coordinate with muscles and sensory feedback to generate motor behaviors appropriate to an animal's environment. In C. elegans, the mechanisms by which the motor circuit generates undulations and modulates them based on the environment are largely unclear. We quantitatively analyzed C. elegans locomotion during free movement and during transient optogenetic muscle inhibition. Undulatory movements were highly asymmetrical with respect to the duration of bending and unbending during each cycle. Phase response curves induced by brief optogenetic inhibition of head muscles showed gradual increases and rapid decreases as a function of phase at which the perturbation was applied. A relaxation oscillator model based on proprioceptive thresholds that switch the active muscle moment was developed and is shown to quantitatively agree with data from free movement, phase responses, and previous results for gait adaptation to mechanical loadings. Our results suggest a neuromuscular mechanism underlying C. elegans motor pattern generation within a compact circuit. [ABSTRACT FROM AUTHOR]

An on-chip nanopower RC relaxation oscillator is developed in a 180-nm standard CMOS process, consuming 300 nW while running at 10 kHz. Employing a frequency compensation scheme that reduces the frequency drift introduced by comparator offset and delay, the proposed oscillator achieves a significant low temperature coefficient. Furthermore, a supply regulation structure is used to reduce the frequency sensitivity to supply voltage variations. Post-simulation results show that the frequency variation against temperature is 105 ppm/ ∘ C in the temperature range from 0 to 85 ∘ C, and the line sensitivity is 2.19%/V with the supply voltage changing from 1.05 to 1.45 V. At offset frequencies of 100 Hz and 1 kHz, the simulated phase noises are −50 and −71 dBc/Hz, respectively. [ABSTRACT FROM AUTHOR]

This paper proposes a numerical method for solving fractional relaxation-oscillation equations. A relaxation oscillator is a type of oscillator that is based on how a physical system returns to equilibrium after being disrupted. The primary equation of relaxation and oscillation processes is the relaxation-oscillation equation. The fractional derivatives in the relaxation-oscillation equations under consideration are defined in the Φ -Caputo sense. The numerical method relies on a novel type of operational matrix method, namely, the Φ -Haar wavelet operational matrix method. The operational matrix approach has a lower computational complexity. The proposed scheme simplifies the main problem to a set of linear algebraic equations. Numerical examples demonstrate the validity and applicability of the proposed technique. [ABSTRACT FROM AUTHOR]

Computing with networks of synchronous oscillators has attracted wide-spread attention as novel materials and device topologies have enabled realization of compact, scalable and low-power coupled oscillatory systems. Of particular interest are compact and low-power relaxation oscillators that have been recently demonstrated using MIT (metal-insulator-transition) devices using properties of correlated oxides. Further the computational capability of pairwise coupled relaxation oscillators has also been shown to outperform traditional Boolean digital logic circuits. This paper presents an analysis of the dynamics and synchronization of a system of two such identical coupled relaxation oscillators implemented with MIT devices. We focus on two implementations of the oscillator: (a) a D-D configuration where complementary MIT devices (D) are connected in series to provide oscillations and (b) a D-R configuration where it is composed of a resistor (R) in series with a voltage-triggered state changing MIT device (D). The MIT device acts like a hysteresis resistor with different resistances in the two different states. The synchronization dynamics of such a system has been analyzed with purely charge based coupling using a resistive (RC) and a capacitive (CC) element in parallel. It is shown that in a D-D configuration symmetric, identical and capacitively coupled relaxation oscillator system synchronizes to an anti-phase locking state, whereas when coupled resistively the system locks in phase. Further, we demonstrate that for certain range of values of RC and CC, a bistable system is possible which can have potential applications in associative computing. In D-R configuration, we demonstrate the existence of rich dynamics including non-monotonic flows and complex phase relationship governed by the ratios of the coupling impedance. Finally, the developed theoretical formulations have been shown to explain experimentally measured waveforms of such pairwise coupled relaxation oscillators. [ABSTRACT FROM AUTHOR]

In this article, we propose two kinds of electrical interconnect test methods for production tests and field ones of assembled circuit boards, which are performed prior to and after shipping to market, respectively. For these tests, we also propose a built-in test circuit. The methods we followed are based on the oscillation frequency of a relaxation oscillator (ROsc) embedded in integrated circuits (ICs). The frequency is measured as the number of pulse signals within a specified test time. Using the test methods, open defects at the interconnects between IC pins and a printed circuit board (PCB) are detected that are modeled as a resistor, a capacitor, and an open-circuit fault. We examined the detectability of open defects using the process variations afforded by SPICE simulation. The simulation results show that open defects were detected, modeled as a resistor of 45.8 Ω or above, along with open defects modeled as a capacitor and an open-circuit fault using the production test method. In addition, a resistance increase of 1.2 Ω at defect-free interconnects occurred after shipping to market was detected using the field test method. We also prototyped ICs with embedded ROscs and built an experimental circuit made of the ICs on PCBs. Moreover, we experimentally examined whether open defects could be detected. The results show that with the production test method, open defects modeled as a resistor of 10 Ω or above and modeled as a capacitor and an open-circuit fault can be detected. [ABSTRACT FROM AUTHOR]

This paper presents a relaxation oscillator (RxO) utilizing subthreshold transistor leakage current compensation (SLC) technology to expand the operating range from 70 °C to 85 °C at high temperatures. The compensated RxO outperforms the uncompensated counterpart by 25 times for temperature coefficient (TC). Additionally, forward body bias (FBB) technology optimizes the digital buffer delay with temperature drift at low supply voltage, extending the oscillator's low-temperature range from −20 °C to −40 °C. Fabricated in a 65 nm CMOS process, the oscillator consumes a mere 8.1 nW at a 0.4 V supply voltage. At room temperature, it operates at 4.22 kHz with an energy efficiency of 1.92 nW/kHz. The oscillator demonstrates a temperature coefficient (TC) of 114.01 ppm/°C within the range of −40 °C to 85 °C, rendering it a prospective choice for low-power Internet of Things (IoT) applications. [ABSTRACT FROM AUTHOR]

We explore the emergence of a variety of different spatiotemporal patterns in a 2D lattice of self-sustained oscillators, which interact nonlocally through an active nonlinear element. A basic element is a van der Pol oscillator in a regime of relaxation oscillations. The active nonlinear coupling can be implemented by a radiophysical element with negative resistance in its current–voltage curve taking into account nonlinear characteristics (for example, a tunnel diode). We show that such coupling consists of two parts, namely, a repulsive linear term and an attractive nonlinear term. This interaction leads to the emergence of only standing waves with periodic dynamics in time and absence of any propagating wave processes. At the same time, many different spatiotemporal patterns occur when the coupling parameters are varied, namely, regular and complex cluster structures, such as chimera states. This effect is associated with the appearance of new periodic states of individual oscillators by the repulsive part of coupling, while the attractive term attenuates this effect. We also show influence of the coupling nonlinearity on the spatiotemporal dynamics. [ABSTRACT FROM AUTHOR]

The mechanisms underlying the emergence of seizures are one of the most important unresolved issues in epilepsy research. In this paper, we study how perturbations, exogenous or endogenous, may promote or delay seizure emergence. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures. Author summary: Despite its simplicity, the modelling of epileptic dynamics as a slow-fast transition between low and high activity states mediated by some slow feedback variable is a relatively novel albeit fruitful approach. This study is the first, to our knowledge, characterizing the response of such slow-fast models of epileptic brain to perturbations by computing its isochrons. Besides its numerical computation, we theoretically determine which factors shape the geometry of isochrons for planar slow-fast oscillators. As a consequence, we introduce a theoretical approach providing a clear understanding of the response of perturbations of slow-fast oscillators. Within the epilepsy context, this elucidates the origin of the contradictory role of interictal epileptiform discharges in the transition to seizure, manifested by both pro-convulsive and anti-convulsive effect depending on the amplitude, frequency and timing. More generally, this paper provides theoretical framework highlighting the role of the slow flow component on the response to perturbations in relaxation oscillators, pointing to the general phenomena in such slow-fast oscillators ubiquitous in biological systems. [ABSTRACT FROM AUTHOR]

(a) Equivalent circuit Schematic of separate multiple CPEs design. (b) and (c) Relative phase error for different fractional-orders sharing the same capacitive loading with n = 8. [Display omitted] Constant Phase Elements (CPEs) have been widely used in many applications due to the extra degree of freedom, which offers new responses and behaviors. This paper proposes a new programmable CPE realization using resistive crossbar arrays. By programming the resistive devices, different CPEs can be obtained. The proposed realization can be approximated as a weighted sum of low and high pass filters having the same cut-off frequency (i.e., Lapicque model). The closed-form approximation expression is derived, and then the Flower Pollination Algorithm (FPA) is used to find the optimal values of the network components. Different design examples are given over the frequency range of 106-109 rad/sec to prove the ability of this realization achieving any fractional order with less than 5% relative error in both phase and pseudo-capacitance. Monte-Carlo simulations are performed to evaluate the sensitivity of the proposed realization against device variability. In addition, multiple CPEs can be designed at the same time by utilizing the multiple ports of the crossbar array. The proposed realization is compared with two other state-of-art realizations showing comparable results as standalone realization and within fractional-order relaxation oscillator application. The proposed crossbar realization has proven its ability to realize any CPE with acceptable error. In addition, this multiple-port design offers high flexibility and on-the-fly switching of the CPE. [ABSTRACT FROM AUTHOR]

We propose a modular architecture for neuromorphic closed-loop control based on bistable relaxation oscillator modules consisting of three spiking neurons each. Like its biological prototypes, this basic component is robust to parameter variation but can be modulated by external inputs. By combining these modules, we can construct a neural state machine capable of generating the cyclic or repetitive behaviors necessary for legged locomotion. A concrete case study for the approach is provided by a modular robot constructed from flexible plastic volumetric pixels, in which we produce a forward crawling gait entrained to the natural frequency of the robot by a minimal system of twelve neurons organized into four modules. [ABSTRACT FROM AUTHOR]

The article provides information on a study which examined first-order synchronization transition in a large population of strongly coupled relaxation oscillators. Topics discussed include description on chemical micro-oscillators, role of natural frequency distribution, and synchronization mechanism for relaxation oscillators.

This article proposes simple relaxation-oscillator-based digital interfacing schemes for resistive sensors in single-element and quarter-bridge forms. The proposed interfaces, equipped with novel compensation techniques, render a direct-digital output proportional to sensor resistance. These interfaces offer many meritorious features, such as simplicity of design, nonrequirement of the reference voltage, lower execution time, and negligible influences from circuit nonidealities. The methodology of the interfaces and their design criteria and error analysis are described in this article. The first two interfaces are suitable for nonremote resistive sensors, while the third interface has been developed for remotely located resistive sensors. The functionality of the proposed interfaces has been verified using simulation as well as detailed experimental studies. The developed interfaces provide a linear direct-digital output, and the maximum experimental nonlinearity is merely 0.08%. Later, a representative sensor based on the giant magnetoresistance (GMR) phenomenon is selected, characterized, and tested with the developed interfaces. The complete instrumentation system is shown to act as a linear digital magnetometer. Finally, the performance of the developed interfaces is compared and shown to be better/comparable with respect to the existing works. [ABSTRACT FROM AUTHOR]

The authors in this article present the synthesis of good quality CuGaGeSe4 thin films of different thicknesses using electron beam deposition on well pre-cleaned glass substrates. X-ray diffraction patterns displayed the amorphous nature of as-prepared CuGaGeSe4 thin films. In addition, the elemental compositional analysis of these films was examined by the energy-dispersive X-ray spectroscopy technique, which showed that there is good matching between the selected and detected percentages. Transmittance and reflectance spectra of these CuGaGeSe4 samples were measured to experimentally determine the absorption coefficient and some related optical parameters. Optical band-gap energy values of samples were determined via Tauc's Plots; they are arisen owing to the indirect allowed transition. They are decreased from 1.43 to 1.29 eV by increasing the film thickness from 250 to 445 nm. The skin depth, absorption index, and refractive index of CuGaGeSe4 thin films were also obtained and extensively studied. As well as, some optoelectrical parameters of these investigated films were discussed, like optical resistivity, optical mobility, optical conductivity, the lattice dielectric constant, and the ratio of the charge carrier concentrations to the effective mass (Nopt/m*). Along with, some nonlinear optical parameters of CuGaGeSe4 films were studied employing Miller's formulas. The values of the dispersion energy, static refractive index, the static dielectric constant, the oscillator strength and others increase, while the oscillator energy and the relaxation time decrease as the film thickness increased. The obtained results showed that these CuGaGeSe4 film samples can be successfully used as absorption layers in thin-film solar cells. [ABSTRACT FROM AUTHOR]

The design of a 22 KHz 358 nW CMOS relaxation oscillator with a process and temperature compensation scheme is presented. Instead of the commonly used RC time constant, the oscillation period of the proposed circuit is determined by the resistance ratio of several resistors, which is insensitive to process and temperature variations. The on-chip relaxation oscillator is simulated in a 0.18 μ m CMOS process. Without any calibration or off-chip components, the frequency variation of the proposed oscillator is ± 3.24% across − 2 0 ∘ C to 100 ∘ C temperature range and 5 different process corners. Compared to the conventional relaxation oscillator, the frequency variation of this circuit is reduced by 89%. The simulated temperature coefficient is 111 ppm/ ∘ C, and the frequency variation over the supply voltage from 1.2 V to 1.7 V is 2.1%/V. The typical power consumption of the proposed circuit is 358 nW. [ABSTRACT FROM AUTHOR]

Reported herein is the mixed metal–insulator phase induced in needle‐like VO2 single crystals by direct current (DC) electric currents applied at ambient temperature; it appears in the current‐controlled negative differential resistivity (CC‐NDR) regime of the nonlinear I–V characteristic governed by self‐heating. In this regime, the I–V characteristic is stable for RL ≥ |dV/dI|max, (RL—the load resistance); for lower RL, portions of I–V are unstable and switching occurs between initial and final steady states (SSs). In high‐quality needle‐like VO2 single crystals (cross‐sectional area < 2 × 10−5 cm2) the SS NDR regime is "unique," whereas crossing from the insulating to the mixed phase I(V) is almost—or perfectly—smooth, the dissipation power (P = IV) versus current bends and this bend is accompanied by the appearance of insulating domains sliding along the metallic background in the sense of the current. The periodic domain emission, the variation of the dynamic parameters (domains' frequency and sliding velocity) over the steady‐state NDR regime, and the energetics of the process are discussed. These results show that the process of domain emission and sliding is fairly expensive at low frequencies but there is some evidence that the process becomes more efficient at higher frequencies. [ABSTRACT FROM AUTHOR]

Two-stroke relaxation oscillations consist of two distinct phases per cycle—one slow and one fast—which distinguishes them from the well-known van der Pol-type 'four-stroke' relaxation oscillations. This type of oscillation can be found in singular perturbation problems in non-standard form, where the slow-fast timescale splitting is not necessarily reflected in a slow-fast variable splitting. The existing literature on such non-standard problems has developed primarily through applications—we complement this by illustrating the suitability of a more general framework for geometric singular perturbation theory to prove existence and uniqueness for a general class of two-stroke relaxation oscillators. While this result can be derived from a more general result in de Maesschalck et al (2011 Indagationes Math. 22 165–206), our methods emphasise the scope, simplicity and applicability of this non-standard approach. We apply this non-standard geometric singular perturbation toolbox to a collection of examples arising in the dynamics of nonlinear transistors and models for mechanical oscillators with friction. [ABSTRACT FROM AUTHOR]

This paper describes a technique to detect blood cell levels based on the time-period modulation of a relaxation oscillator loaded with an Inter-Digitated Capacitor (IDC). A digital readout circuit has been proposed to measure the time-period difference between the two oscillators loaded with samples of healthy and (potentially) unhealthy blood. A prototype circuit was designed in 65-nm CMOS technology and post-layout simulations show 15.25-aF sensitivity. The total circuit occupies 2,184- μ m2 silicon area and consumes 216 μ A from a 1-V power supply. [ABSTRACT FROM AUTHOR]

In bacteria, cell polarization involves the controlled targeting of specific proteins to the poles, defining polar identity and function. How a specific protein is targeted to one pole and what are the processes that facilitate its dynamic relocalization to the opposite pole is still unclear. The Myxococcus xanthus polarization example illustrates how the dynamic and asymmetric localization of polar proteins enable a controlled and fast switch of polarity. In M. xanthus , the opposing polar distribution of the small GTPase MglA and its cognate activating protein MglB defines the direction of movement of the cell. During a reversal event, the switch of direction is triggered by the Frz chemosensory system, which controls polarity reversals through a so-called gated relaxation oscillator. In this review, we discuss how this genetic architecture can provoke sharp behavioral transitions depending on Frz activation levels, which is central to multicellular behaviors in this bacterium. [ABSTRACT FROM AUTHOR]

We use simulations and dynamical systems tools to investigate the mechanisms of generation of phase-locked and localized oscillatory cluster patterns in a globally coupled Oregonator model where the activator receives global feedback from the inhibitor, mimicking experimental results observed in the photosensitive Belousov-Zhabotinsky reaction. A homogeneous two-cluster system (two clusters with equal cluster size) displays antiphase patterns. Heterogenous two-cluster systems (two clusters with different sizes) display both phase-locked and localized patterns depending on the parameter values. In a localized pattern the oscillation amplitude of the largest cluster is roughly an order of magnitude smaller than the oscillation amplitude of the smaller cluster, reflecting the effect of self-inhibition exerted by the global feedback term. The transition from phase-locked to localized cluster patterns occurs as the intensity of global feedback increases. Three qualitatively different basic mechanisms, described previously for a globally coupled FitzHugh-Nagumo model, are involved in the generation of the observed patterns. The swing-and-release mechanism is related to the canard phenomenon (canard explosion of limit cycles) in relaxation oscillators. The hold-and-release and hold-and-escape mechanisms are related to the release and escape mechanisms in synaptically connected neural models. The methods we use can be extended to the investigation of oscillatory chemical reactions with other types of non-local coupling. [ABSTRACT FROM AUTHOR]

A fully-integrated 2.9 MHz RC relaxation oscillator is presented in this paper. In order to eliminate performance degradation caused by propagation delay at low power, the delay equivalent electric charges technique based on comparator offset cancellation structure is utilized. The oscillator is designed in 180 nm CMOS process and 1-point trimmed to operate within 0.2% precision by a specific mathematical model. With core area of 0. 115 mm 2 , the oscillator achieves a frequency stability of 45 ppm/°C in range from −40 ∼ +125 °C and demonstrates an energy efficiency of 2.49 μ W/MHz. [ABSTRACT FROM AUTHOR]

We have observed relaxation oscillations in an argon capacitive discharge connected to a peripheral grounded chamber through a slot with dielectric spacers. The oscillations, observed from time-varying optical emission of the main discharge chamber, show, for example, a high frequency (∼40 kHz) relaxation oscillation at 100 mTorr, with absorbed power near that for peripheral breakdown, and a low frequency (∼3 Hz) oscillation, at higher absorbed power. The high frequency oscillation is found to ignite a plasma in the slot, but usually not in the periphery. We interpret the high frequency oscillations using an electromagnetic model of the slot impedance, coupled to a circuit analysis of the system including the matching network. The model results are in general agreement with the experimental observations and indicate a variety of behaviors dependent on the matching conditions. [ABSTRACT FROM AUTHOR]

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe the VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by and Mikami and Okazaki [J. Chem. Phys. 121, 10052 (2004)] invoking the path-integral influence functional method with the second order cumulant expansion. We apply our formulas to VER of the amide I mode of a small amino-acid like molecule, N-methylacetamide, in heavy water. [ABSTRACT FROM AUTHOR]

[Display omitted] • Detailed study of laser-induced oxidation of vanadium enables synthesis of laser-written VO2 spots and lines. • Reversible phase transition of VO 2 observed in power dependent Raman measurements. • Voltage & temperature induced resistance switching of laser written VO 2 is observed. • Complete two terminal V-VO 2 -V device along with isolation fabricated using laser. • Relaxation oscillator based on fabricated VO 2 device is demonstrated. Vanadium Dioxide (VO 2) changes reversibly from metal and insulator phase around the transition temperature (68 °C) causing resistance and reflectance switching. Conventional VO 2 device fabrication technology involves VO 2 deposition, lithography for film patterning/etching, and contact formation. The overall fabrication process is complex, time-consuming, costly, and requires harmful chemicals. This work demonstrates a lithography-free method to fabricate VO 2 devices where the VO 2 region synthesis, isolation, and contact formation are all done in continuity using direct laser writing (DLW) on Vanadium (V) thin films. The effect of the laser parameters on oxidation is examined and spots of phase pure VO 2 and V 2 O 5 are obtained on the same sample, with VO 2 showing ∼ 2 orders of resistance switching. Lines of VO 2 are synthesized using DLW on V film, resulting in a V-VO 2 -V structure which after laser isolation forms a completely laser-written VO 2 device exhibiting resistance switching driven by either voltage or temperature. To display the suitability of the fabricated device for circuit applications, a relaxation oscillator circuit is demonstrated. The presented DLW based lithography free approach to synthesize VO 2 structures and devices significantly simplifies fabrication compared to traditional semiconductor processing approaches. It can also enable single step fabrication of integrated circuits based on vanadium oxide active regions with V interconnects. [ABSTRACT FROM AUTHOR]

We present detailed analytical and experimental results for a system of two comparator-based relaxation oscillators that are coupled via threshold modulation. Starting with the op-amp circuit equations, we derive parameter conditions that lead to n:1 phase-locked solutions, thereby obtaining predictions for the shapes of Arnold tongues for this system. These tongues are compared to experimental data and good agreement is found. We follow up with a stability analysis of phase-locked solutions. Specifically, we use two-timescale asymptotic analysis, and we check some results obtained therein against experimentally captured dynamics. [ABSTRACT FROM AUTHOR]

Transient electronic absorption measurements reveal the vibrational relaxation dynamics of CH3I following excitation of the C–H stretch overtone in the gas phase and in liquid solutions. The isolated molecule relaxes through two stages of intramolecular vibrational relaxation (IVR), a fast component that occurs in a few picoseconds and a slow component that takes place in about 400 ps. In contrast, a single 5–7 ps component of IVR precedes intermolecular energy transfer (IET) to the solvent, which dissipates energy from the molecule in 50 ps, 44 ps, and 16 ps for 1 M solutions of CH3I in CCl4, CDCl3, and (CD3)2CO, respectively. The vibrational state structure suggests a model for the relaxation dynamics in which a fast component of IVR populates the states that are most strongly coupled to the initially excited C–H stretch overtone, regardless of the environment, and the remaining, weakly coupled states result in a secondary relaxation only in the absence of IET. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The quantum dynamics of an anharmonic oscillator coupled to a bath of up to 60 harmonic oscillators is investigated by a new multiconfigurational hybrid method for wave packet propagation. The method, originally proposed in [Burghardt, Meyer, and Cederbaum, J. Chem. Phys. 111, 2927 (1999)], represents a variant of the multiconfiguration time-dependent Hartree method including a moving basis of Gaussian functions. Energy relaxation and quantum decoherence induced by the zero-temperature oscillator bath are shown to be accurately described by the new method. Decoherence rates for a bath with a discretized ohmic spectral density are found to be consistent with golden-rule predictions for T=0. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]