scholarly journals The dynamics of synchronization of two-stage van der Pol generator

2021 ◽  
Vol 24 (3) ◽  
pp. 56-62
Author(s):  
Valery V. Zaitsev ◽  
Alexander V. Karlov
Keyword(s):  
Discrete System ◽  
Autonomous System ◽  
Harmonic Signal ◽  
Frequency Characteristics ◽  
Synchronous Oscillation ◽  
Van Der Pol ◽  
Two Stage ◽  
Synchronization Process ◽  
Complex Oscillation ◽  
Synchronous Oscillations

Results of numerical simulation of self-oscillations synchronization process in two-cascade ring generator van der Pol by harmonic signal are presented. Studies were carried out within the framework of the DT- model of the dynamic system. The model was developed on the basis of the principle of compliance within the framework of the method of slowly changing amplitudes of characteristics of a discrete system with characteristics of an analog prototype. Shortened equations for complex oscillation amplitudes in generator stages are obtained. It was found that in an autonomous system there is an effect of bistability of amplitudes. In the synchronization mode with an external harmonic signal, solutions of shortened equations made it possible to calculate amplitude-frequency and phase-frequency characteristics of synchronous oscillations. It is shown that transitions between bistable states are observed in the synchronous oscillation holding band. Differences of frequency characteristics of synchronization of classical and two-stage oscillators van der Pol were analyzed.

scholarly journals Frequency characteristics of the fractional oscillator Van der Pol

2019 ◽  
Vol 127 ◽  
pp. 02010
Author(s):  
Roman Parovik
Keyword(s):  
Quality Factor ◽  
Harmonic Balance ◽  
Fractional Derivatives ◽  
Harmonic Balance Method ◽  
Oscillatory System ◽  
Frequency Characteristics ◽  
Van Der Pol ◽  
Fractional Oscillator ◽  
Analytical Formulas ◽  
Frequency Phase

Into this paper, the amplitude-frequency and phase-frequency characteristics of the Van der Polar fractional oscillator are studied in order to establish their relationship with the orders of fractional derivatives included in the model equation. Using the harmonic balance method, analytical formulas were obtained for the amplitude-frequency, phase-frequency characteristics, as well as the quality factor – the energy characteristic of the oscillatory system. It was shown that the quality factor depends on the orders of fractional derivatives, and change in their values can lead to both an increase and a decrease in the quality factor.

scholarly journals DYNAMICS OF ELASTIC EXCITABLE MEDIA

1999 ◽  
Vol 09 (11) ◽  
pp. 2197-2202 ◽  
Author(s):  
JULYAN H. E. CARTWRIGHT ◽  
VÍCTOR M. EGUÍLUZ ◽  
EMILIO HERNÁNDEZ-GARCÍA ◽  
ORESTE PIRO
Keyword(s):  
Viscous Friction ◽  
Excitable Media ◽  
Elastic Coupling ◽  
Van Der Pol ◽  
Frictional Sliding ◽  
Friction Law ◽  
Synchronous Oscillations ◽  
Earthquake Faults ◽  
Sliding Dynamics ◽  
Low Dimensional

The Burridge–Knopoff model of earthquake faults with viscous friction is equivalent to a van der Pol–FitzHugh–Nagumo model for excitable media with elastic coupling. The lubricated creep–slip friction law we use in Burridge–Knopoff model describes the frictional sliding dynamics of a range of real materials. Low-dimensional structures including synchronous oscillations and propagating fronts are dominant, in agreement with the results of laboratory friction experiments. Here we explore the dynamics of fronts in elastic excitable media.

scholarly journals DYNAMICS OF SELF-OSCILLATIONS IN A TWO-STAGE VAN DER POL OSCILLATOR

2017 ◽  
Vol 19 (6) ◽  
pp. 141-146
Author(s):  
V.V. Zaitsev ◽  
S.V. Lindt ◽  
I.V. Stulov
Keyword(s):  
Numerical Simulation ◽  
Spatial Distribution ◽  
Van Der Pol Oscillator ◽  
Ring Oscillator ◽  
Van Der Pol ◽  
Two Stage ◽  
Generation Threshold

The results of numerical simulation of self-oscillations in a two-stage ring oscillator with active cells of Van der Pol are presented. It is shown that for large exceedances of generation threshold in a system with identical cells, non-uniform spatial distribution of amplitudes of self-oscillations is observed.

BIFURCATION AND CHAOS IN COUPLED BVP OSCILLATORS

2004 ◽  
Vol 14 (04) ◽  
pp. 1305-1324 ◽  
Author(s):  
TETSUSHI UETA ◽  
HISAYO MIYAZAKI ◽  
TAKUJI KOUSAKA ◽  
HIROSHI KAWAKAMI
Keyword(s):  
Autonomous System ◽  
Period Doubling ◽  
Chaotic Attractors ◽  
Nonlinear Phenomena ◽  
Van Der Pol ◽  
Bifurcation And Chaos ◽  
Experimental Laboratory ◽  
Chaotic Parameter ◽  
Parameter Values ◽  
The Mathematical Model

Bonhöffer–van der Pol(BVP) oscillator is a classic model exhibiting typical nonlinear phenomena in the planar autonomous system. This paper gives an analysis of equilibria, periodic solutions, strange attractors of two BVP oscillators coupled by a resister. When an oscillator is fixed its parameter values in nonoscillatory region and the others in oscillatory region, create the double scroll attractor due to the coupling. Bifurcation diagrams are obtained numerically from the mathematical model and chaotic parameter regions are clarified. We also confirm the existence of period-doubling cascades and chaotic attractors in the experimental laboratory.

Bifurcation Control for a Kind of Non-Autonomous System with Time Delay

2010 ◽  
Vol 34-35 ◽  
pp. 1752-1756
Author(s):  
Chang Zhao Qian ◽  
Zhi Wen Wang ◽  
Chuang Wen Dong ◽  
Yang Liu
Keyword(s):  
Time Delay ◽  
Perturbation Method ◽  
Time Delays ◽  
Autonomous System ◽  
Primary Resonance ◽  
Stable Region ◽  
Bifurcation Equation ◽  
Van Der Pol ◽  
Average Equation ◽  
System With Time Delay

A forced van der Pol system with two time-delays is studied. The central aim is analyzing primary resonance of this system. Perturbation method is used to obtain the average equation and bifurcation equation with time-delays. Based on the average equation, the stable region of this system is discussed. Based on the bifurcation equation, the multivalued property of response amplitude is studied. The result indicates that this system can be well controlled with time delays.

Research of Sub-Synchronous Oscillations in HVDC and SSDC Designing

2014 ◽  
Vol 960-961 ◽  
pp. 1062-1067
Author(s):  
Han Chen ◽  
Chun Lin Guo ◽  
Qin Lei Chen ◽  
Zhe Ci Tang ◽  
Ya Nan Li ◽  
...  
Keyword(s):  
Simulation Model ◽  
Compensation Method ◽  
Frequency Range ◽  
Synchronous Oscillation ◽  
Phase Compensation ◽  
Frequency Scanning ◽  
Synchronous Oscillations ◽  
Electrical Damping ◽  
Oscillation Damping ◽  
Damping Controller

SSDC(Supplementary sub-synchronous oscillation damping controller) is one of effective measures to suppress the SSO(sub-synchronous oscillations) caused by HVDC. The article researched the phase compensation method of SSDC on the basis of studying the SSO and the SSDC mechanism in depth. We verified the validity of the method used by designing SSDC in an large domestic HVDC simulation model. And we find that the SSDC designed can effectively increase the positive electrical damping in the sub-synchronous frequency range with the sub-synchronous frequency scanning to suppress the SSO.

scholarly journals Application of the α-approximation for discretization of analogue systems

2005 ◽  
Vol 18 (3) ◽  
pp. 571-586 ◽  
Author(s):  
Tomislav Sekara ◽  
Milic Stojic
Keyword(s):  
Comparative Analysis ◽  
Discrete System ◽  
Discretization Error ◽  
Frequency Characteristics ◽  
Approximation Methods ◽  
Frequency Range ◽  
Discretization Methods ◽  
Basic Frequency ◽  
Analogue System ◽  
Transformation Methods

The method for discretization of analogue systems using the ?-approximation is presented. A generalization of some of the existing transformation methods is also done. A comparative analysis, through the corresponding examples involving several known discretization methods, is carried out. It is demonstrated that the application of this ?-approximation allows the reduction of discretization error compared to other approximation methods. The frequency characteristics of the discrete system obtained by these transformations are approximately equal to these of the original analogue system in the basic frequency range.

scholarly journals Synchronization, oscillator death, and frequency modulation in a class of biologically inspired coupled oscillators

2018 ◽  
Author(s):  
Alessio Franci ◽  
Marco A Herrera-Valdez ◽  
Miguel Lara-Aparicio ◽  
Pablo Padilla-Longoria
Keyword(s):  
Circadian Clock ◽  
Coupled Oscillators ◽  
Deterministic Model ◽  
Nonlinear Models ◽  
Biological Rhythms ◽  
Planck Equation ◽  
General Mechanism ◽  
Synchronous Oscillation ◽  
Synchronous Oscillations ◽  
Do So

The general purpose of this paper is to build up on our understanding of the basic mathematical principles that underlie the emergence of synchronous biological rhythms, in particular, the circadian clock. To do so, we study the role that the coupling strength, coupling type, and noise play in the synchronization of a system of coupled, nonlinear oscillators. First, we study a deterministic model based on Van der Pol coupled oscillators, modeling a population of diffusively coupled cells, to find regions in the parameter space for which synchronous oscillations emerge and to provide conditions under which diffusive coupling kills the synchronous oscillation. Second, we study how noise and coupling interact and lead to synchronous oscillations in linearly coupled oscillators, modeling the interaction between various pacemaker populations, each having an endogenous circadian clock. To do so, we use the Fokker-Planck equation associated to the system. We show how coupling can tune the frequency of the emergent synchronous oscillation, which provides a general mechanism to make fast (ultradian) pacemakers slow (circadian) and synchronous via coupling. The basic mechanisms behind the generation of oscillations and the emergence of synchrony that we describe here can be used to guide further studies of coupled oscillations in biophysical nonlinear models.

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