Self-oscillating System Research Articles

Calculating Mixed Forced and Self-Oscillations for Delayed Elastic Constraint and a Limited Power Energy Source

A frictional self-oscillating system with an elastic force delay and external influence is considered while interacting with an energy source of limited power. The procedure for using direct linearization methods to calculate mixed forced oscillations and self-oscillations in a system with delay and limited excitation is described. Based on this procedure, equations of nonstationary and stationary motion are derived.

Vehicle’s transmission as a vibro-impact system

The article discusses a dynamic model of a dual-clutch transmission. The absence of a torque converter and the short duration of gear shifting (0.2 - 0.5 sec) in such transmissions allows to present the shifting process as impact interaction. As a result, the gear shift excites the oscillations of the gearbox output shaft. Thus, the transmission of the vehicle can be considered as a vibro-impact self-oscillating system.

Analysis of Self-oscillating Single-acting Hydro-impact System Operational Modes with Two Limiters of Striker Movement

A new property of self-oscillating single-acting hydro-impact systems is considered in this paper – an ability to make strikes in forward and backward directions in presence of two limiters of striker movement without structural changes in device. Mathematical models are presented for system, which includes a flow rate source, a control valve, an impact unit (body frame, striker and spring), an energy accumulator and two limiters. Program for system operational modes (op-modes) simulation is developed and dynamics of specific typical device is numerically investigated. Theoretical oscillograms of its dynamic characteristics and dependencies of integral characteristics on source and impact device parameters are analyzed. At low flow rate multiimpact self-oscillating cycles are obtained, in which the nature of dynamics phenomenon repeats after several striker-limiters interactions. Increase of flow rate leads to single-impact working mode with forward direction of striker movement, then to transition to double-impact mode with forward and backward directions and, further, to single-impact mode with backward direction. Transition boundary points, in which system op-modes changes, are found. Results of this paper can be applied in development of reversible hydro-impact devices (with impacts in forward and backward directions) for mining and construction engineering.

Stability of Periodic Motions and Synthesis of Relay Sampled Data Control Systems

This article is devoted to research and design of relay systems with control of data sampling. It is shown that the time sample has a significant effect on the parameters of periodic oscillations. We propose an exact method for analyzing periodic modes in digital self-oscillatory control systems with a two-position relay element and a linear piecewise-linear part is proposed. The proposed approach extends the phase hodograph method to the class of systems operating in discrete time. Two approaches have been developed to assess the stability of periodic motions in such systems. In the first approach, a discrete representation of a plant is considered and areas of stability are defined for each possible limit cycle. The sampling of the control system causes a delay in the switching of the relay in a batch mode in comparison with the continuous case. The second approach assumes the replacement of a discrete system by an equivalent continuous system with a time delay. Further, the asymptotic orbital stability of self-oscillations in a relay control system (RCS) with a delay is estimated. We consider the linearization of relay systems with digital control of the input signal. It is also shown that when linearizing a relay element in a digital RCS using a useful signal, the relay transfer ratio will belong to a certain range of values. Synthesis of corrective devices for relay control systems with regard to digital implementation has been reviewed. At the stage of optimization of parameters of the relay control system, the sample is taken into account. The model example demonstrates an advantage in the synthesis of digital technologies. It is shown that when optimizing the controller parameters with regard to time discretization, it was possible to provide the desired frequency of self-oscillations, which ensures the best accuracy of the tracking mode.

Численное моделирование влияния электромагнитных импульсов на работу типовых электронных автоколебательных систем.

Численное моделирование влияния электромагнитных импульсов на работу типовых электронных автоколебательных систем.

THE PREDICTOR-CORRECTOR METHOD FOR MODELLING OF NONLINEAR OSCILLATORS

In the work physically reasonable algorithm of numerical modeling of nonlinear oscillatory and self-oscillatory systems are offered. The algorithm is based on discrete in time model of the linear oscillator. Nonlinearity is considered by the introduction to the oscillator of additional communications by the structural analysis of an initial system. For approximation of a temporary derivative in nonlinear communications it is offered to use the scheme of the prediction and correction. In spite of the fact that theoretically the algorithm has the second order of accuracy, within the numerical experiment with Van der Pol oscillator it shows better results, than a standard method of the second order the Heuns method.

Stochastic thermodynamics of self-oscillations: the electron shuttle

Self-oscillation is a phenomenon studied across many scientific disciplines, including the engineering of efficient heat engines and electric generators. We investigate the single electron shuttle, a model nano-scale system that exhibits a spontaneous transition towards self-oscillation, from a thermodynamic perspective. We analyse the model at three different levels of description: The fully stochastic level based on Fokker–Planck and Langevin equations, the mean-field (MF) level, and a perturbative solution to the Fokker–Planck equation that works particularly well for small oscillation amplitudes. We provide consistent derivations of the laws of thermodynamics for this model system at each of these levels. At the MF level, an abrupt transition to self-oscillation arises from a Hopf bifurcation of the deterministic equations of motion. At the stochastic level, this transition is smeared out by noise, but vestiges of the bifurcation remain visible in the stationary probability density. At all levels of description, the transition towards self-oscillation is reflected in thermodynamic quantities such as heat flow, work and entropy production rate. Our analysis provides a comprehensive picture of a nano-scale self-oscillating system, with stochastic and deterministic models linked by a unifying thermodynamic perspective.

The predictor-corrector method for modelling of self-oscillatory systems

In the work physically reasonable algorithm of numerical modeling of nonlinear oscillatory and self-oscillatory systems is offered. The algorithm is based on discrete in time model of the linear oscillator. Nonlinearity is considered by introduction to the oscillator of additional communications by the structural analysis of an initial system. For approximation of a temporary derivative in nonlinear communications it is offered to use the scheme of the prediction and correction. In spite of the fact that theoretically the algorithm has the second order of accuracy, within the numerical experiment with Van der Pol oscillator it shows the best results, than a standard method of the second order – the Heun’s method.

The discrete biharmonic model of Thomson self-oscillators

For modeling of self-oscillations in generators of Thomson type the numerical-analytic method is offered. The method is based on representation of self-oscillatory system in the form of set of two oscillators - the main frequency and its third harmonica. The leading oscillator generates strictly monochromatic self-oscillations in discrete time and excites on the oscillator of the third harmonica. The main attention is paid to self-oscillations in three-point schemes with capacitor and inductive communications. It is shown that the offered method of modeling allows to give comparative estimates of amplitudes of harmonious components of a spectrum of self-oscillations.

Серцево-респіраторна система як система з обмеженим збудженням

A new modified cardiorespiratory model based on the famous DeBoer beat-to-beat model and Zaslavsky map (which describes dynamics of the respiratory system as a generator of central type) was studied in details. In this case the respiratory tract was firstly modeled by a self-oscillating system under the impulsive influence of heartbeat and cardiovascular system was represented as an oscillating system with a limited excitation. The steady-state regimes of the model are investigated by methods of the dynamical system theory. Firstly, the chaotic regimes were found out. The dynamics of heartbeat and respiratory systems are in good correspondence with experimental information of healthy man. The found out irregularities of phase trajectories of the modified model depend on intensity of influence of heart rhythm on breathing, what is well known characteristic for the dynamics of the cardiovascular system of healthy man.

Генерация импульсов гигантской амплитуды в клистронном автогенераторе хаоса

The presented experimental results demonstrate the formation of giant amplitude microwave impulses by a chaotic klystron generator operating in autonomous mode. The auto-oscillator is constructed on the basis of a “noisetron” scheme, which contains two five-resonator drift klystrons connected in series in a ring. One of the klystrons operates in a signal linear amplification mode (a linear klystron) and the other - in a signal nonlinear amplification mode (a nonlinear klystron). It has been established that a regime of dynamic intermittency of the “chaos-chaos” type appears in a self-oscillating system at a certain value of a beam current of the nonlinear klystron. In this case, the chaotic sequences of microwave impulses of giant amplitude are formed on a chaotic amplitude background. This type of intermittency is due to the amplitude bistability of the nonlinear klystron.

The Oretical and Experimental Aspects of Building a Model of the Self-Oscillatory Wave Wind Turbine

The article presents an overview of the work on the creation of a mathematical model of self-oscillating systems for converting the energy of the moving flow of the medium. The principle of their work and their inherent advantages are described. The method of measurement and processing of the array of kinematical data during the operation of the wind turbine is considered. The evaluation of the efficiency of self-oscillating wind turbines is given.

MODEL OF SELF-OSCILLATIONS WITHOUT HARMONICAS OF THE BASE FREQUENCY

The nonlinearity of self-oscillatory system limiting amplitude of the generated signal is a source of the higher harmonicas of the base frequency. Harmonicas distort a form of self-oscillations and lower stability of their frequency. In the work the mathematical model of generation of self-oscillations, free from the highest harmonicas strictly monochromatic self-oscillations is offered. The model is based on a method of equivalent (harmonious) linearization, popular in the applied theory of nonlinear oscillations. Numerical realization of the model in discrete time has allowed to formulate two algorithms of generation of monochromatic self-oscillations. One of them includes the procedure of numerical integration of a Cauchy problem for the system of ordinary differential equations. Another reproduces processes in the discrete dynamic system designed on analog model-prototype. The monochromaticity of discrete self-oscillations is confirmed within the numerical experiment.

Nonlinear Dynamics, Quasi-Periodic Summation, Self-Oscillating Processes, and Information Coding in Selective Spiking Neural Networks

Nonlinear dynamics, physical processes, and information processing in selective spiking neurons are investigated. Summation of pulse inputs are considered on the basis of the theory of quasi-periodic functions and nonlinear transformation via relaxation of the self-oscillating system of a neuron. A way of encoding input information is also considered in which the information unit is a pulse sequence, and the intensity of the input signal is encoded by a synchronous change in the frequency of the pulse sequences.

GEOMETRIA ED ELASTICITÀ: FOLDING DI UN SOLIDO, DRIPPING DI UN’ASTA ELASTICA E STRUTTURE SELF-OSCILLATING

The leitmotiv of the described research activity is the situation in which an elastic solid or an elastic structure can spontaneously generate complex geometrical patterns, when subjected to extreme deformation. In this context, folding and faulting are described for a three-dimensional elastic solid with extreme anisotropy. The dripping of an elastic rod is presented (as generated by configurational forces) and finally the possibility of a self-oscillating elastic system is introduced, where an elastic structure oscillates with a given frequency when subject to a steady energy input.

The influences of the ionic channel conductances and kinetics on the phase-locking behaviors of modeled sinoatrial node cells and tissue

Sinoatrial node (SAN) is the leading pacemaker of the heart, whose pathologies are closely associated to certain kinds of arrhythmias. Phase-locking is a characteristic behavior of the self-oscillatory SAN system, which is relevant to the heart rate modulation. It is known that the SAN phase-locking properties are influenced by the stimulating magnitude, the stimulated site in the tissue, the intercellular coupling strength and even the couplings from the atrial cells. Besides the above knowledge, a practical problem remains undiscussed, i.e., the influences of the channel conductances and kinetics on the phase-locking property. In the present paper a detailed electrophysiological SAN model is investigated. The effects of several major parameters modulating the channels' conductances and the time constants are illustrated. We find that the phase-locking ranges depend on the automaticity of the system. Any parameter variation slowing down the intrinsic oscillating rate may increase the phase-locking ranges, while that speeding up the rate may shrink them. The well known phase resetting property is applied to explain the phenomena, founding on which the analytical formulas for estimating the phase-locking ranges are derived.

Cluster analysis of cardiac data

The article includes the observation of the cluster analysis of medical data on the example of the cardiac data. One of the main effective and commonly used Data Mining methods that applied to the large amounts of information (for example, mathematical economics) are clustering methods: the search for signs of similarity between objects in the study of the subject area and the subsequent merger of objects into subsets (clusters) according to the established affinity. The main purpose of the investigation is to examine the hypothesis of the possibility of diagnosing the patient health status, as well as identifying his pathologies, using the analysis of electrocardiogram (ECG) series and the allocation of similar clusters based on the results of this analysis. However, the subject of clustering techniques implementation to the ECG on the grounds of similarity of forms have not previously been extensively investigated. In the model of the heart, which is used in this study, the state of the heart is taken as a fixed oscillatory process of the phenomenon of the FPU auto-return. But, on the other hand, since the heart is an self-oscillating system and it has no need to start the oscillations by obtaining the energy of “perturbation”, the concept of FPU autoreturn is introduced in the study of the heart. The mathematical modeling of the heart work by using a decomposition of the Fermi-Pasta-Ulam (FPU) was investigated. The formal description of the mathematical model of the heart as a system of connected cells myocytes is presented. This represents a single oscillatory degree of freedom described by a system of coupled nonlinear differential equations of the second order equation of Van der Pol. Cluster analysis bases on the search of similar clusters of Fourier spectrum which are received by FPU recurrence. The current results that are obtained show that the hypothesis is confirmed. In mathematical modeling of the FPU heart modeling, which is based on the forms of Fourier spectra, were identified. Subsets were identified, among which various subsets of both forms of Fourier spectra with pathologies and forms of the Fourier spectrum of healthy people were formed. From this study it follows that the cluster analysis of the electrocardiogram may refer this ECG to any cluster and thereby diagnose the state of cardiac health of the patient.

The emergence of multistability and chaos in a two-mode van der Pol generator versus different connection types of linear oscillators

In this work, we study the multistability and chaos phenomena in a classical two-mode van der Pol generator which consists of a nonlinear element and two linear oscillators. We show that the configuration of the connections of the linear oscillators in the two-mode self-oscillating system significantly affects its oscillation regimes and bifurcational transitions. In the case of the feedback loop including one oscillator, the two-mode system demonstrates the well-known effect of frequency entrainment, including bistability and hysteresis phenomena. If the feedback loop involves both linear oscillators, the entrainment effect disappears; however, two new complex regimes of quasi-periodicity and chaotic self-oscillations emerge. We present here the results of the bifurcation analysis of the multistability formation and transition to chaos.

Quantum effects in amplitude death of coupled anharmonic self-oscillators.

Coupling two or more self-oscillating systems may stabilize their zero-amplitude rest state, therefore quenching their oscillation. This phenomenon is termed "amplitude death." Well known and studied in classical self-oscillators, amplitude death was only recently investigated in quantum self-oscillators [Ishibashi and Kanamoto, Phys. Rev. E 96, 052210 (2017)2470-004510.1103/PhysRevE.96.052210]. Quantitative differences between the classical and quantum descriptions were found. Here, we demonstrate that for quantum self-oscillators with anharmonicity in their energy spectrum, multiple resonances in the mean phonon number can be observed. This is a result of the discrete energy spectrum of these oscillators, and is not present in the corresponding classical model. Experiments can be realized with current technology and would demonstrate these genuine quantum effects in the amplitude death phenomenon.

Dynamics of a Self-Oscillatory System with an Energy Source

The interaction of a self-oscillatory system with an energy source of limited power is considered. By direct linearization, a formula is derived for calculating the dynamic parameters.