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This paper studies global output feedback stabilization (OFS) control for non-strict feedback nonlinear systems with unknown functions (UFs). In order to deal with the UFs problem, a Lemma is proposed. This Lemma not only avoids the disadvantages of approximation methods, but also avoids the Assumptions of UFs. Therefore, the algorithm in the paper reduces the conservatism. Then, a control algorithm is proposed to solve the global OFS control problem of closed-loop systems. At the same time, the “explosion of terms” problem of backstepping is also solved. Finally, the algorithm is applied to Duffing system and Chua’s oscillator system to verify the effectiveness of the algorithm.

The inertial element, damping element and elastic element are the main components of a mechanical oscillation system. The values of these elements affect the resonant frequency of the mechanical system in a MEMS vibratory gyroscope. Besides, it is a necessary factor to determine the operating frequency of the mechanical system. In the mechanical system of the MEMS vibratory gyroscope, the elastic elements such as the elastic beams are directly connected with the proof-mass. The typical dynamic parameters of the oscillator system need to be determined to study the vibration characteristics of the MEMS vibratory gyroscope with some initial conditions. The construction of modeling and calculation of the dynamic parameters of a crab-shaped MEMS vibratory gyroscope which consists of a proof-mass with 2 in-plane degree-of-freedoms realized in this paper.

In this paper, a new type of ultrasonic vibration de-gluing device has been designed to remove the cured epoxy resin adhesive that overflowed from the aluminum alloy structural parts in the high-speed train carriages. At present, manual removal is used to remove the cured epoxy resin adhesive that overflows at the bonding site. This method has low removal efficiency and leads to poor surface quality of the parts. The new type of ultrasonic vibration de-gluing device can solve these problems. Modal analysis and harmonic response analysis are carried out on the ultrasonic vibration oscillator system in the ultrasonic vibration de-gluing device, and the reasonable structure parameters and resonance frequency of the ultrasonic vibration oscillator system are determined. Finally, the impedance test and de-gluing effect test are carried out on the prototype of the ultrasonic vibration de-gluing device to verify the feasibility and practicability of the new type of ultrasonic vibration de-gluing device. The results show that the ultrasonic vibration de-gluing device’s stable resonant operating frequency is 28,270 Hz, and the average error between the simulation and experimental results of the resonant operating frequency is less than 3%, which validates the simulation model.

Problems involving vibrations (mechanical or electrical) can be reduced to problems of coupled oscillators. For this, we consider the motion of coupled oscillators system using Lagrangian method. The Lagrangian of the system was initially constructed, and then the Euler-Lagrange equations (i.e., equations of motion of the system) have been obtained. The obtained equations of motion are a homogenous second-order equation. These equations were solved numerically using the ode45 code, which is based on Runge-Kutta method.

Exact eigenstate solutions of Schrodinger equation for a generalized oscillator system that includes, as special cases; ring shaped oscillator potential and isotropic harmonic oscillator potential are examined in an analytical treatment by using extended Nikiforov Uvarov method. Radial and angular parts of the Schrodinger equation for the relevant potential can be systematically solved in the same manner. Moreover the relation between the eigenfunction solutions for this potential and Heun polynomials are presented. (C) 2021 Elsevier B.V. All rights reserved., Scientific and Technological Research Council of Turkey [121F014], This study has been supported by Scientific and Technological Research Council of Turkey with the grant number 121F014.

We study the effect of quantum entanglement maintained by virtual excitations in an ultrastrongly-coupled harmonic-oscillator system. Here, the quantum entanglement is caused by the counterrotating interaction terms and hence it is maintained by the virtual excitations. We obtain the analytical expression for the ground state of the system and analyze the relationship between the average excitation numbers and the ground-state entanglement. We also study the entanglement dynamics between the two oscillators in both the closed- and open-system cases. In the latter case, the quantum master equation is microscopically derived in the normal-mode representation of the coupled-oscillator system. This work will open a route to the study of quantum information processing and quantum physics based on virtual excitations., 13 pages, 6 figures

This article presents a control design method for asymptotic stabilization, synchronization, and antisynchronization of a five dimensional chaotic memristor oscillator system. Two cases are conside...

This paper explores exponential synchronization and phase locking of a Kuramoto-oscillator network with multi-harmonic coupling functions. In the presence of pacemaker and distributed controllers, such a Kuramoto-oscillator network is a multilayer system, and we present several conditions to achieve exponential synchronization and phase locking. We estimate the lower bounds for the synchronization and phase locking rate of such a multilayer Kuramoto-oscillator network. Finally an example of the multilayer system illustrates the effectiveness of the theoretical results.

In this paper, the effect of random parameter on the boundary crisis of the smooth and discontinuous oscillator system is studied. First of all, we convert this stochastic system into a high-dimensional equivalent deterministic system by means of the orthogonal polynomial approximation. Afterward, the method of composite cell coordinate system is used to exhibit the global dynamical behavior of this system in different state spaces. Then, the attractors, basins of attraction and saddles of this system are obtained. We find that there exists interesting boundary crisis phenomenon in this system and the randomness of parameter has an obvious effect on it. Finally, we make a conclusion that the random parameter could suppress the boundary crisis of this system.

10.1119/1.5095945.1We describe a simple experiment observing oscillations of fluid in a drinking straw immersed in a bath of water. The motion of this oscillator system with changing mass is matched remarkably well by a model derived from Newton's laws with the inclusion of only a phenomenological damping coefficient. We compare the frequency of the oscillations to Hooke's law for small displacements and find 0.25% discrepancy. This experiment can be shown as a demonstration of oscillations of fluids, or it can be performed by students as a laboratory activity in upper-division undergraduate physics and engineering courses.

The entanglement dynamics in a bipartite system consisting of a qubit and a harmonic oscillator interacting only through their coupling with the same bath is studied. The considered model assumes that the qubit is coupled to the bath via the Jaynes-Cummings interaction, whilst the position of the oscillator is coupled to the position of the bath via a dipole interaction. We give a microscopic derivation of the Gorini-Kossakowski-Sudarshan-Lindblad equation for the considered model. Based on the Kossakowski Matrix, we show that non-classical correlations including entanglement can be generated by the considered dynamics. We then analytically identify specific initial states for which entanglement is generated. This result is also supported by our numerical simulations., Comment: 15 pages, 8 figures, Accepted in Open Systems & Information Dynamics for publication

Emergence of distinct collective dynamical states in the two smallest populations of nonlinear oscillators with global coupling among them is delineated. In particular, considering four oscillators constituting two populations of two oscillators each, we show the emergence of local chimera, global chimera, and global amplitude chimera states by breaking the permutation symmetry within the populations, in addition to the local synchronized and global synchronized states. Further, the symmetry breaking facilitates the onset of local chimera accompanied by the anomalous synchronization even with an identical nonisochronicity parameter in contrast to the existing literature. Furthermore, the spread of local synchronized and local chimera states is found to increase upon increasing the frequency difference among the populations, while the spread of local chimera, global chimera, and global amplitude chimera states increases for larger values of the nonisochronicity parameter. In addition, we have also deduced the stability condition for the global synchronized state using both the amplitude and its phase model, and find that the global synchronized state attains stability even for smaller values of the coupling strength for the amplitude model when compared to its phase reduced model.

In this study, a single-step additive manufacturing approach to fabricate an array of bio-inspired soft whisker-like sensors is presented. Each whisker is a damped oscillator system that is tuned to a different resonant frequency whose response is characterized through experimentation in an air medium. A 3 × 1 polymer based whisker-array is used to distinguish individual frequency components in mixed-frequency signals, achieving a form of “mechanical Fourier transform”

In this paper, we present a two-layer coupled oscillator model, in which the first layer is composed of the nearest neighbor coupled identical oscillator, the second layer is composed of the global coupled identical oscillator, and there is a one-way point-to-point drive from the second layer to the first layer. In this system, the driven layer changes from unsynchronized state to synchronized state with the change of parameters. During this transformation, we found the existence of chimer state. And the dynamic behavior of the system had been studied. The critical value for the state transition had been caught.

The transverse relaxation time τ2 of the built-in alkali metal magnetometer is an important parameter to characterize its performance and the working state of the nuclear magnetic resonance (NMR) oscillator system. The method we propose to measure τ2 is to apply the frequency-scanning magnetic fields along the x-axis and obtain τ2 from the 3 dB bandwidth of the measured x-axis amplitude–frequency response curve of the magnetometer. We give a detailed and rigorous theoretical derivation by using the perturbation-iteration method to demonstrate the rationality of this measuring method. Then, both the actual experiment and the simulation experiment results are presented to verify the validity and good accuracy of the method. All the sampled frequencies in the scanning range should be far away from both the 129Xe and 131Xe NMR frequencies, to avoid introducing any influence on the nuclear spins; therefore, this method can provide a non-interference way for measurement of τ2, helping us monitor the NMR oscillator system’s state under normal operating conditions.

In this paper, the variance of fatigue damage under stationary random loadings is investigated by means of different case studies (linear oscillator system, random process with ideal unimodal or bimodal power spectral density). Monte Carlo method is used to evaluate the variance of fatigue damage in time-domain and frequency-domain approach. The variance from simulations is compared with analytical methods (e.g. Mark and Crandall’s method, Bendat’s method and Low’s method). Furthermore, for each case study, the paper investigates the relationship between the variance of fatigue damage and the bandwidth parameters. The purpose is to provide a simple closed-form solution for the case of ideal unimodal power spectral density. The closed-form solution has been compared with Monte Carlo simulation in time-domain. The results show good agreement not only for narrow-band but also for wide-band process.

Vibrational resonance is studied in a fractional order quintic oscillator system with delayed feedback. By utilizing the perturbation theory, the theoretical approximate expression of the response amplitude at low-frequency is obtained. In the presence of fractional order and time delay, resonance phenomena are studied in the single-well, double-well and triple-well potentials, respectively. Meanwhile, the good agreement between theoretical prediction and numerical simulation verifies the validity of theoretical analysis. It is found that by altering the fractional order derivative, the occurrence of new resonances is more frequent. As delay increases, the bifurcation point and the equilibrium point change periodically. In addition, fractional order, time delay feedback and high-frequency force amplitude can be appropriately selected to achieve the goal of maximizing the output in different systems. In particular, an intersection that affects the triple-well potential bifurcation point was found.

In real environment, the impulsive control signals can’t be input accurately, because there are always some input errors while realizing the stabilization of memristor-based oscillator system. Thus, it is very important to consider the small time window in the process of impulsive control. That is the occurrence of impulse in each control cycle is limited by small impulse time window. On the other hand, It is necessary to do some research on the chaotic memristor oscillator systems due to the potential applications of memristor. Based on linear matrix inequality, Lyapunov stability theory, and impulsive control with time window, the exponential stability conditions for one type of hyperchaotic smooth memristor oscillator system are displayed. Finally, simulation results show the feasibility and effectiveness of this impulsive stabilization method.

In this paper, we investigate the problem of conformation change in a network of coupled oscillator system with double well internal potential. Conformation change refers to the phenomena where all the oscillators in the network make a transition from one potential well to another potential well under the influence of external perturbation. We propose a novel approach based on information transfer in network dynamical systems to understand this phenomenon. We consider a heterogeneous network system where the internal dynamics of the oscillators are assumed to be nonidentical and the interconnecting Laplacian can also be asymmetric. The objective is to determine which of the network oscillator is most influential in driving the conformation dynamics. We show that the net information transfer of individual oscillators can be used to determine the most influential oscillator which can drive the entire network from one well to another well of the potential. We use three different network topologies to verify our proposed framework.

In this paper, we consider a delay-coupled neural oscillator system with inhibitory-to- inhibitory connection. The effects of coupled weights and multiple delays are analyzed. It follows that the increasing coupled weights bring out the multiple coexistences of stable and unstable equilibria by a cascade of pitchfork bifurcations. Moreover, multiple delays control the unstable equilibria to stable periodic solutions. Thus, neural oscillator system exhibits the multiperiodicity coexistences. To this end, we firstly study the equilibria properties and give some equilibria patterns. Analyzing the multiple pitchfork bifurcations of trivial and nontrivial equilibria respectively, we find that there are one, three, five and nine equilibria for the increasing coupled weight. The neural system has a single trivial equilibrium and pairs of synchronous or anti-synchronous nontrivial equilibria, which exhibits the multiple equilibria coexistences. Secondly, employing the corresponding characteristic equation, the effects of coupled delays on stable and unstable equilibria are studied. We find that the stable equilibria keep their stability for the increasing delay, which is called the delay-independent stability. However, for the unstable equilibria, coupled delay suppresses system trajectories near these equilibria into some stable periodic solutions. Therefore, the neural oscillator system exhibits the stability coexistences with multiple equilibria and multiperiodicities.

In this chapter, a novel two-raft wave energy absorption device is proposed to seek new ways of improving the power capture capacity and investigated with a numerical method.

We examine theoretically and measure experimentally the instability regions for a pair of parametrically driven mechanical oscillators on an air track. We take the position of the second mass, multiply it by cos (ω_Dt), and apply it to the first mass. We show that this leads to an instability for both normal modes of the coupled oscillator system when ω_D is close to the difference of the normal mode frequencies. Such an instability mechanism is of special interest because the input frequency, ω_D, can be much lower than the output frequencies of the system. In addition, we consider the case where cos (ω_Dt) is replaced by a negative constant, which also leads to instability, but at a single frequency. This study of the difference frequency oscillator system was motivated by the QASER system described in Svidzinsky, Yuan and Scully [Phys. Rev. X 3, 041001 (2013)].

We demonstrate a hybrid oscillator system that combines the tunability of spin torque oscillators (STOs) with the exceptional quality factor (Q) of a high-overtone bulk acoustic resonator (HBAR) in a 2-chip system. The demonstrated magneto-acoustic oscillator (MAO) has a tuning range of 5% at 4 GHz with 175 kHz 3 dB linewidth. When compared to STOs we achieve a 200χ reduction in linewidth, while retaining the original tuning range.

Summary In this paper, we consider the problem of disturbance response and error amplification for a simple system of coupled harmonic oscillators. We first suppose that identical oscillators are connected in a string in which each oscillator attempts to track its predecessor by using the same control law that depends on the relative position information from its immediate predecessor. Such an oscillator string is called a homogeneous oscillator string with predecessor-following architecture. Motivated by terminology from the problem of vehicle platooning, we say that the synchronized oscillator system is string unstable if the effect of a disturbance to the lead oscillator is amplified as it propagates along the string. With the use of a new Bode-like integral relation that must be satisfied by the complementary sensitivity function, we provide sufficient conditions for string instability. The sufficient conditions show that any string of oscillators that satisfies certain time domain performance specifications and bandwidth limitations must necessarily be string unstable. We further introduce a concept of time headway for the oscillator system and extend our analysis of string instability to consider the heterogeneous oscillator string and a more general communication range. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, some coupled retarded systems on networks (CRSNs) are studied. Applying the idea of Razumikhin method and Mirchhoff’s matrix tree theorem, the sufficient conditions for global exponential stability of the CRSNs are obtained. Finally, an example of coupled retarded oscillator system on networks is given to illustrate the advantages of our results.

A new wave number based approach is proposed for the evaluation of the time-domain Green's function for the railway track idealized as an infinite Euler-Bernoulli beam overlying a Pasternak-type viscoelastic foundation. In the proposed approach, the rail beam response is first computed in the time wave number domain by solving a generalized single-degree-of-freedom system problem using the classical Duhamel integral technique. The Green's function is subsequently evaluated by inverting the so-obtained time wave number solution to the time-space domain. In contrast with the conventional approach, the computational time for evaluating the Green's function using the proposed approach is much smaller. Further, the proposed solution of the Green's function is shown to be convenient for directly evaluating the time-domain response of a rail beam subjected to various types of time-dependent loads. As an illustration, the Green's function is applied to obtain the time-domain response of the rail beam (overlying a viscoelastic layer) subjected to a uniformly moving oscillator by using a novel and simple two-step iterative scheme. The time-domain deflection analysis reveals that the introduction of damping into the oscillator system brings the rail beam response much closer to that associated with the constant moving load idealization. However, if the moving oscillator system is acted upon by an arbitrarily time-varying external vertical load, significantly higher values of rail beam deflections are observed.

We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasi-periodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is derived using the Ott-Antonsen ansatz. The applicability of the ansatz is checked by the comparison of numerical results of the coupled oscillator system and the reduced low-dimensional equation. We investigate further several interesting phenomena in which mutual interactions between the fast and slow oscillators play an essential role. Fast oscillations appear intermittently as a result of excitatory interactions with slow oscillators in a certain parameter range. Slow oscillators experience an oscillator-death phenomenon owing to their interaction with fast oscillators. This oscillator death is explained as a result of saddle-node bifurcation in a simple phase equation obtained using the temporal average of the fast oscillations. Finally we show macroscopic synchronization of the order 1:m between the slow and fast oscillators., 10 pages, 10 figures

A brief review of the Surface Acoustic Wave (SAW)-based gas sensors and their physical operation background in a dual-delay line oscillator system is presented together with some own achievements dealing with SAW layered sensor structures.

We investigate the fundamental connection between quadrature squeezing and continuous variable entanglement within a general class of two-coupled oscillator systems. We determine the quantitative relationship between them through the squeezing parameter and the entanglement entropy of the lowest energy eigenstate of the coupled oscillator systems numerically. Unlike the relation between entanglement and uncertainty product, we found that this relationship is, by no means, the same for the whole class of coupled oscillator systems: to a large extent it depends on the order and strength of the anharmonic potential, which implies that knowledge of the anharmonic potential of the coupled oscillator system is required before one can characterize the degree of entanglement through the squeezing parameter. Our results reveal that a more effective approach to enhance squeezing is to adjust the anharmonicity of the system potential, instead of increasing the quantum correlations between the oscillators. In addition, by probing into a quantum catastrophe model, we uncover transitions in the entanglement entropy and squeezing relation as the potential changes from a single well to a triple well, and then a double-well structure. The transitions appear through distinct entropy–squeezing relation, with a multi-well structure displaying a larger change in the antisqueezing behavior of the position quadrature than the single-well structure, for the same change in the entanglement entropy.

We consider a Fabry–Perot cavity with one fixed mirror and a movable perfectly reflecting mirror. Applying a linearised fluctuation analysis, we derive the quantum fluctuations and correlation matrix between the cavity and nanomechanical oscillator. We investigate the continuous-variable (CV) entanglement and squeezing between the cavity and nanomechanical oscillator. It is found that high intensity of entanglement and squeezing between the cavity and nanomechanical oscillator can be achieved.

The development of a nuclear spin oscillator system, namely a spin maser with an external feedback, for use in the search for 129Xe atomic EDM is presented. By introducing a new current source for the B0 field solenoid, drifts in the maser frequency were remarkably suppressed. This in turn clearly brought out the correlation between the maser frequency and the environmental field. Correcting for the effect of the environmental field, the frequency precision of 5 nHz in the measurement time of 45,000 s was attained. Origins of the remaining drifts in the maser frequency are now under investigation.

In this paper, distributed systems that consist of many locally-connected subsystems, especially oscillators, and produce linear state relations, such as a state dierence, are treated. The relations are defined between two connected subsystems, where their references are also assigned as a goal behavior simultaneously. The problem is: how subsystem dynamics are constructed to converge the relations to their references by only use of local operations, and how these references are adjusted if they are unachievable. To solve the above problems, a mathematical description of the subsystem interactions are clarified by extending a method based on the gradient dynamics. Then, the reference adjustment is defined so that the subsystem interactions decreases. As an example of this formulation, the relative phase control of the circularly coupled oscillator system is considered, where the oscillation with the uniform phase lag should be achieved. This oscillator system is applied to the timing controller for the multi-cylinder engine, and its eectiveness is

This paper proposes a new type of memristor with two distinct stable pinched hysteresis loops and twin symmetrical local activity domains, named as a bistable bi-local active memristor. A detailed and comprehensive analysis of the memristor and its associated oscillator system is carried out to verify its dynamic behaviors based on nonlinear circuit theory and Hopf bifurcation theory. The local-activity domains and the edge-of-chaos domains of the memristor, which are both symmetric with respect to the origin, are confirmed by utilizing the mathematical cogent theory. Finally, the subcritical Hopf bifurcation phenomenon is identified in the subcritical Hopf bifurcation region of the memristor.

This paper is concerned with the problems of global stabilization and restricted tracking for a multiple oscillator system by bounded feedback. A nonlinear feedback law consisting of nested saturation functions is proposed to achieve global stabilization. To improve the transient performance of the closed-loop system, the parameters in this feedback law can be tuned to assign the poles of the closed-loop system when none of the saturation elements in the control law is in effect. The proposed feedback law is also shown to achieve restricted tracking. Simulation results are given to show the effectiveness of the proposed feedback law.

In this paper, a nonlinear oscillator with discontinuity is analyzed using He’s amplitude–frequency formulation. The natural frequency of the oscillator system can be obtained using concise and straightforward calculation steps. Good agreement between the results from the proposed and other classical approaches is reached.

There was a mix-up of Figs. 6+7 and 8+9 in the initial online publication. The original article has been corrected.

A system of two magnets hung from two vertical springs and oscillating in the hollows of a pair of coils connected in series is a new, interesting and useful example of coupled oscillators. The electromagnetically coupled oscillations of these oscillators are experimentally and theoretically studied. Its coupling is electromagnetic instead of mechanical, and easily adjustable by the experimenter. The coupling of this new coupled oscillator system is determined by the currents that the magnets induce in two coils connected in series, one to each magnet. It is an interesting case of mechanical oscillators with field-driven coupling, instead of mechanical coupling. Moreover, it is both a coupled and a damped oscillating system that lends itself to a detailed study and presentation of many properties and phenomena of such a system of oscillators. A set of experiments that validates the theoretical model of the oscillators is presented and discussed.

The time-independent quantal sudden theory of vibrational excitation is presented for a collinear system. A new semiclassical sudden theory is also obtained directly from the quantal theory by simply replacing quantal oscillator wavefunctions by their JWKB approximations. For the atom-harmonic oscillator system with the Jackson-Mott interaction potential, closed-form expressions are obtained for the quantal and semiclassical scattering matrices. The unitarity of the quantal and semiclassical S matrices and the conditions for the validity of the sudden approximation are discussed.

We formulate the statistical mechanics of chaotic system with few degrees of freedom and investigated the quartic oscillator system using microcanonical and canonical ensembles. Results of statistical mechanics are numerically verified by considering the dynamical evolution of quartic oscillator system with two degrees of freedom.