scholarly journals Period Doubling with Hysteresis in BL Her-Type Models

1993 ◽  
Vol 134 ◽  
pp. 301-305
Author(s):  
P. Moskalik ◽  
J. R. Buchler
Keyword(s):  
Regular Solution ◽  
Limit Cycles ◽  
Fundamental Mode ◽  
Narrow Range ◽  
Period Doubling ◽  
Light Curves ◽  
Hydrodynamical Models ◽  
Stable Period ◽  
Classical Cepheids ◽  
The Stability

We have performed recently a survey of the nonlinear hydrodynamical models of the BL Her-type variables (Buchler & Moskalik 1992). Within this project we have studied several sequences of models, i.e., families in which onlyTeff has been varied from model to model, while all other stellar parameters have been kept constant. The fundamental mode pulsations of each model have been converged to strict periodicity with the relaxation code (Stellingwerf 1974). Such approach speeds up the calculations and simultaneously yields information about the stability properties of the resulting limit cycles. In all studied sequences except one, we have found a narrow-range of Teff (typically 100-150K), in which regular solution becomes unstable towards a period doubling bifurcation. The instability has its origin in a half-integer resonance, namely the 3:2 coupling between the fundamental mode and the first overtone (cf. Moskalik & Buchler 1990; hereafter MB90). This is the same resonance, which also causes period doubling in the models of classical Cepheids (Moskalik & Buchler 1991). The bifurcation leads to stable period-two oscillations, characterized by an RV Tau-like, albeit strictly periodic behavior of all variables. In other words, the pulsation light curves and velocity curves will exhibit two alternating minima (as well as maxima) of different values.

Period-Luminosity-Shape of Light Curve Relation for Cepheids in LMC and SMC

2005 ◽  
Vol 201 ◽  
pp. 480-481
Author(s):  
P. Ligeza ◽  
P. Moskalik ◽  
A. Schwarzenberg-Czerny
Keyword(s):  
Light Curve ◽  
Principal Components Analysis ◽  
Principal Components ◽  
Fundamental Mode ◽  
Light Curves ◽  
Analysis Of Covariance ◽  
Curve Shape ◽  
Long Period ◽  
Classical Cepheids ◽  
Components Analysis

In this paper we report our analysis of the period-luminosity-shape of light curve (P-L-S) relation. The data we used came from LMC and SMC Cepheid light curves produced by OGLE-II microlensing survey. We used Principal Components Analysis of covariance matrix of the sets for Cepheids in LMC and SMC separately. Our calibrating set was bounded to long period classical Cepheids pulsating in fundamental mode. The results are used to derive a method for estimation of distances from light curve shape.

scholarly journals A New Possible Resonance for Population II Cepheids

1985 ◽  
Vol 82 ◽  
pp. 250-253
Author(s):  
A. N. Cox ◽  
R. B. Kidman
Keyword(s):  
Fundamental Mode ◽  
Variable Stars ◽  
Light Curves ◽  
Radial Mode ◽  
Classical Cepheids

Light and velocity curves of some radial mode variable stars seem to indicate a resonance where the second overtone has a period exactly half that of the fundamental mode. The two classes of stars that show this resonance by bumps in their light curves are the classical Cepheids and the population II BL Her variables. We here propose that there is another resonance for the population II W Vir variables where the ratio of the first overtone to the fundamental periods is 0.5.

scholarly journals DC-DC Zeta Power Converter: Ramp Compensation Control Design and Stability Analysis

2021 ◽  
Vol 11 (13) ◽  
pp. 5946
Author(s):  
David Angulo-García ◽  
Fabiola Angulo ◽  
Juan-Guillermo Muñoz
Keyword(s):  
Power Systems ◽  
Duty Cycle ◽  
Extreme Values ◽  
Period Doubling ◽  
Power Converter ◽  
Large Set ◽  
Compensation Control ◽  
Stable Period ◽  
Wide Range ◽  
The Stability

The design of robust and reliable power converters is fundamental in the incorporation of novel power systems. In this paper, we perform a detailed theoretical analysis of a synchronous ZETA converter controlled via peak-current with ramp compensation. The controller is designed to guarantee a stable Period 1 orbit with low steady state error at different values of input and reference voltages. The stability of the desired Period 1 orbit of the converter is studied in terms of the Floquet multipliers of the solution. We show that the control strategy is stable over a wide range of parameters, and it only loses stability: (i) when extreme values of the duty cycle are required; and (ii) when input and reference voltages are comparable but small. We also show by means of bifurcation diagrams and Lyapunov exponents that the Period 1 orbit loses stability through a period doubling mechanism and transits to chaos when the duty cycle saturates. We finally present numerical experiments to show that the ramp compensation control is robust to a large set of perturbations.

scholarly journals Bifurcations and Synchronization of the Fractional-Order Bloch System

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Honggang Dang ◽  
Lixin Yang
Keyword(s):  
Fractional Order ◽  
Limit Cycles ◽  
System Parameter ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
Unknown Parameters ◽  
The Rich ◽  
Period Limit ◽  
The Stability

In this paper, bifurcations and synchronization of a fractional-order Bloch system are studied. Firstly, the bifurcations with the variation of every order and the system parameter for the system are discussed. The rich dynamics in the fractional-order Bloch system including chaos, period, limit cycles, period-doubling, and tangent bifurcations are found. Furthermore, based on the stability theory of fractional-order systems, the adaptive synchronization for the system with unknown parameters is realized by designing appropriate controllers. Numerical simulations are carried out to demonstrate the effectiveness and flexibility of the controllers.

Turning Dynamics: Part 1 — Experimental Analysis

2012 ◽  
Author(s):  
Eric B. Halfmann ◽  
C. Steve Suh ◽  
N. P. Hung
Keyword(s):  
Instantaneous Frequency ◽  
Period Doubling ◽  
Displacement Sensor ◽  
Laser Displacement Sensor ◽  
Turning Process ◽  
Time Frequency ◽  
Spectral Components ◽  
Tool Vibrations ◽  
Exact Moment ◽  
The Stability

The workpiece and tool vibrations in a lathe are experimentally studied to establish improved understanding of cutting dynamics that would support efforts in exceeding the current limits of the turning process. A Keyence laser displacement sensor is employed to monitor the workpiece and tool vibrations during chatter-free and chatter cutting. A procedure is developed that utilizes instantaneous frequency (IF) to identify the modes related to measurement noise and those innate of the cutting process. Instantaneous frequency is shown to thoroughly characterize the underlying turning dynamics and identify the exact moment in time when chatter fully developed. That IF provides the needed resolution for identifying the onset of chatter suggests that the stability of the process should be monitored in the time-frequency domain to effectively detect and characterize machining instability. It is determined that for the cutting tests performed chatters of the workpiece and tool are associated with the changing of the spectral components and more specifically period-doubling bifurcation. The analysis presented provides a view of the underlying dynamics of the lathe process which has not been experimentally observed before.

scholarly journals Zero Average Surface Controlled Boost-Flyback Converter

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 57
Author(s):  
Juan-Guillermo Muñoz ◽  
Fabiola Angulo ◽  
David Angulo-Garcia
Keyword(s):  
Duty Cycle ◽  
Period Doubling ◽  
Power Converter ◽  
Control Technique ◽  
Average Surface ◽  
Flyback Converter ◽  
Stable Period ◽  
Period 2 ◽  
Wide Range ◽  
The Right

The boost-flyback converter is a DC-DC step-up power converter with a wide range of technological applications. In this paper, we analyze the boost-flyback dynamics when controlled via a modified Zero-Average-Dynamics control technique, hereby named Zero-Average-Surface (ZAS). While using the ZAS strategy, it is possible to calculate the duty cycle at each PWM cycle that guarantees a desired stable period-1 solution, by forcing the system to evolve in such way that a function that is constructed with strategical combination of the states over the PWM period has a zero average. We show, by means of bifurcation diagrams, that the period-1 orbit coexists with a stable period-2 orbit with a saturated duty cycle. While using linear stability analysis, we demonstrate that the period-1 orbit is stable over a wide range of parameters and it loses stability at high gains and low loads via a period doubling bifurcation. Finally, we show that, under the right choice of parameters, the period-1 orbit controller with ZAS strategy satisfactorily rejects a wide range of disturbances.

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

Nonstationary Response of a Two-Degrees-of-Freedom Nonlinear Ship Model Under Modulated Excitation

1995 ◽  
Author(s):  
Ruigui Pan ◽  
Huw G. Davies
Keyword(s):  
Degrees Of Freedom ◽  
Stability Boundary ◽  
Period Doubling ◽  
Approximate Solutions ◽  
Loss Of Stability ◽  
Two Degrees Of Freedom ◽  
Ship Model ◽  
Nonstationary Response ◽  
Period 2 ◽  
The Stability

Abstract Nonstationary response of a two-degrees-of-freedom system with quadratic coupling under a time varying modulated amplitude sinusoidal excitation is studied. The nonlinearly coupled pitch and roll ship model is based on Nayfeh, Mook and Marshall’s work for the case of stationary excitation. The ship model has a 2:1 internal resonance and is excited near the resonance of the pitch mode. The modulated excitation (F0 + F1 cos ωt) cosQt is used to model a narrow band sea-wave excitation. The response demonstrates a variety of bifurcations, loss of stability, and chaos phenomena that are not present in the stationary case. We consider here the periodically modulated response. Chaotic response of the system is discussed in a separate paper. Several approximate solutions, under both small and large modulating amplitudes F1, are obtained and compared with the exact one. The stability of an exact solution with one mode having zero amplitude is studied. Loss of stability in this case involves either a rapid transition from one of two stable (in the stationary sense) branches to another, or a period doubling bifurcation. From Floquet theory, various stability boundary diagrams are obtained in F1 and F0 parameter space which can be used to predict the various transition phenomena and the period-2 bifurcations. The study shows that both the modulation parameters F1 and ω (the modulating frequency) have great effect on the stability boundaries. Because of the modulation, the stable area is greatly expanded, and the stationary bifurcation point can be exceeded without loss of stability. Decreasing ω can make the stability boundary very complicated. For very small ω the response can make periodic transitions between the two (pseudo) stable solutions.

scholarly journals The stability of major and trace element concentrations from musts to Champagne during the production process

OENO One ◽  
2022 ◽  
Vol 56 (1) ◽  
pp. 29-40
Author(s):  
Robin Cellier ◽  
Sylvain Berail ◽  
Ekaterina Epova ◽  
Julien Barre ◽  
Fanny Claverie ◽  
...  
Keyword(s):  
Trace Elements ◽  
Production Process ◽  
Trace Element ◽  
Narrow Range ◽  
Grape Juice ◽  
Elemental Concentrations ◽  
Element Concentrations ◽  
Production Processes ◽  
Overall Stability ◽  
The Stability

Thirty-nine Champagnes from six different brands originating from the AOC Champagne area were analyzed for major and trace element concentrations in the context of their production processes and in relation to their geographical origins. Inorganic analyses were performed on the must (i.e., grape juice) originating from different AOC areas and the final Champagne. The observed elemental concentrations displayed a very narrow range of variability. Typical concentrations observed in Champagne are expressed in mg/L for elements such as K, Ca, Mg, Na, B, Fe, A, and Mn. They are expressed in µg/L for trace elements such as Sr, Rb, Ba, Cu, Ni, Pb Cr and Li in decreasing order of concentrations. This overall homogeneity was observed for Sr and Rb in particular, which showed a very narrow range of concentrations (150 < Rb < 300 µg/L and 150 < Sr < 350 µg/L) in Champagne. The musts contained similar levels of concentration but showed slightly higher variability since they are directly influenced by the bedrock, which is quite homogenous in the AOC area being studied. Besides the homogeneity of the bedrock, the overall stability of the concentrations recorded in the samples can also be directly linked to the successive blending steps, both at the must level and prior to the final bottling. A detailed analysis of the main additives, sugar, yeast and bentonite, during the Champagne production process, did not show a major impact on the elemental signature of Champagne.

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