Jacobi stability analysis and chaotic behavior of nonlinear double pendulum

2017 ◽  
Vol 14 (12) ◽  
pp. 1750176 ◽  
Author(s):  
Shunya Oiwa ◽  
Takahiro Yajima
Keyword(s):  
Stability Analysis ◽  
Lyapunov Stability ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Stable Region ◽  
Physical Parameters ◽  
Double Pendulum ◽  
Mass Ratio ◽  
Unstable Region

In this paper, we study the Jacobi stability on the nonlinear double pendulum by the Kosambi–Cartan–Chern (KCC) theory. We assume that the mass and length of rods of two kinds of pendulums are equal, respectively. Moreover, we consider the case that initial angles of the double pendulum are equal. Under these conditions, we obtain the boundary between Jacobi stable and unstable trajectories for initial angles. It is shown that the condition of Jacobi stable or unstable depends only on deflection angles of the nonlinear double pendulum. Then, we discuss relationships between Jacobi stability, physical parameters and other concepts of stability such as Lyapunov stability and chaos. We suggest that the ratio of length of rods and the mass ratio of pendulums of the double pendulum do not affect the Jacobi stability. It is suggested that the equilibrium points in the Jacobi stable region and in the Jacobi unstable region are Lyapunov stable and Lyapunov unstable, respectively, and that the motions in the Jacobi unstable region are related to the onset of chaotic behavior.

Discontinuous Control and Stability Analysis of Step-Down DC-DC Voltage Converters

2020 ◽  
Vol 38 (3A) ◽  
pp. 446-456
Author(s):  
Bashar F. Midhat
Keyword(s):  
Stability Analysis ◽  
Lyapunov Stability ◽  
Control Method ◽  
Power Electronic ◽  
Electronic Circuits ◽  
Dc Voltage ◽  
Power Electronic Circuits ◽  
Lyapunov Stability Criterion ◽  
Control Step ◽  
Step Down

Step down DC-DC converters are power electronic circuits, which mainly used to convert voltage from a level to a lower level. In this paper, a discontinuous controller is proposed as a control method in order to control Step-Down DC-DC converters. A Lyapunov stability criterion is used to mathematically prove the ability of the proposed controller to give the desired voltage. Simulationsl1 are performedl1 in MATLABl1 software. The simulationl1 resultsl1 are presentedl1 for changesl1 in referencel1 voltagel1 and inputl1 voltagel1 as well as stepl1 loadl1 variations. The resultsl1 showl1 the goodl1 performancel1 of the proposedl1 discontinuousl1 controller.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

Twin stars as tracers of binary evolution in the Kepler era

2021 ◽  
Author(s):  
Sara Bulut ◽  
Baris Hoyman ◽  
Ahmet Dervisoglu ◽  
Orkun Özdarcan ◽  
Ömür Cakilrli
Keyword(s):  
High Resolution ◽  
Internal Structure ◽  
Spectroscopic Analysis ◽  
Independent Method ◽  
Eclipsing Binaries ◽  
Physical Parameters ◽  
Evolutionary Status ◽  
Mass Ratio ◽  
Orbital Parameters ◽  
Binary Evolution

Abstract We present results of the combined photometric and spectroscopic analysis of four systems, which are eclipsing binaries with a twin–component (mass ratio q ≃ 1). These are exceptional tools to provide information for probing the internal structure of stars. None of the systems were previously recognized as twin binaries. We used a number of high–resolution optical spectra to calculate the radial velocities and later combined them with photometry to derive orbital parameters. Temperatures and metallicities of systems were estimated from high-resolution spectra. For each binary, we obtained a full set of orbital and physical parameters, reaching precision below 3 per cent in masses and radii for whole pairs. By comparing our results with PARSEC and MIST isochrones, we assess the distance, age and evolutionary status of the researched objects. The primary and/or secondary stars of EPIC 216075815 and EPIC 202843107 are one of the cases where asteroseismic parameters of δ Sct and γ Dor pulsators were confirmed by an independent method and rare examples of the twin–eclipsing binaries, therefore the following analyses and results concern the pulsating nature of the components.

scholarly journals New Data on the Eclipsing Binary V1848 Ori and Improved Orbital and Light Curve Solutions

2020 ◽  
Vol 29 (1) ◽  
pp. 72-80 ◽  
Author(s):  
Fatemeh Davoudi ◽  
Atila Poro ◽  
Fahri Alicavus ◽  
Afshin Halavati ◽  
Saeed Doostmohammadi ◽  
...  
Keyword(s):  
Binary System ◽  
Light Curve ◽  
Mass Function ◽  
Light Curves ◽  
Complete Analysis ◽  
Physical Parameters ◽  
Mass Ratio ◽  
Third Body ◽  
Eclipsing Binary

AbstractNew observations of the eclipsing binary system V1848 Ori were carried out using the V filter resulting in a determination of new times of minima and new ephemeris were obtained. We presented the first complete analysis of the system’s orbital period behavior and analysis of O-C diagram done by the GA and MCMC approaches in OCFit code. The O-C diagram demonstrates a sinusoidal trend in the data; this trend suggests a cyclic change caused by the LITE effect with a period of 10.57 years and an amplitude of 7.182 minutes. It appears that there is a third body with mass function of f (m3) = 0.0058 M⊙ in this binary system. The light curves were analyzed using the Wilson-Devinney code to determine some geometrical and physical parameters of the system. These results show that V1848 Ori is a contact W UMa binary system with the mass ratio of q = 0.76 and a weak fillout factor of 5.8%. The O’Connell effect was not seen in the light curve and there is no need to add spot.

The effects of drivers’ aggressive characteristics on traffic stability from a new car-following model

2016 ◽  
Vol 30 (18) ◽  
pp. 1650243 ◽  
Author(s):  
Guanghan Peng ◽  
Li Qing
Keyword(s):  
Stability Analysis ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability Analysis ◽  
Stable Condition ◽  
Mkdv Equation ◽  
Stable Region ◽  
Car Following ◽  
Car Following Model ◽  
The Stability

In this paper, a new car-following model is proposed by considering the drivers’ aggressive characteristics. The stable condition and the modified Korteweg-de Vries (mKdV) equation are obtained by the linear stability analysis and nonlinear analysis, which show that the drivers’ aggressive characteristics can improve the stability of traffic flow. Furthermore, the numerical results show that the drivers’ aggressive characteristics increase the stable region of traffic flow and can reproduce the evolution and propagation of small perturbation.

Chaos in the Periodically Parametrically Excited Lorenz System

2021 ◽  
Vol 31 (08) ◽  
pp. 2130024
Author(s):  
Weisheng Huang ◽  
Xiao-Song Yang
Keyword(s):  
Chaotic Dynamics ◽  
Lorenz System ◽  
Stable Equilibrium ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Parametrically Excited ◽  
The Lorenz System

We demonstrate in this paper a new chaotic behavior in the Lorenz system with periodically excited parameters. We focus on the parameters with which the Lorenz system has only two asymptotically stable equilibrium points, a saddle and no chaotic dynamics. A new mechanism of generating chaos in the periodically excited Lorenz system is demonstrated by showing that some trajectories can visit different attractor basins due to the periodic variations of the attractor basins of the time-varying stable equilibrium points when a parameter of the Lorenz system is varying periodically.

scholarly journals Spectroscopic Orbit of the Eclipsing Binary BD +52°2009

1999 ◽  
Vol 170 ◽  
pp. 325-330
Author(s):  
B. Khalesseh
Keyword(s):  
Correlation Function ◽  
Light Curve ◽  
Radial Velocity ◽  
Physical Model ◽  
Cross Correlation ◽  
Cross Correlation Function ◽  
Physical Parameters ◽  
Mass Ratio ◽  
Velocity Measurements ◽  
Eclipsing Binary

AbstractNew radial velocity measurements of the Algol-type eclipsing binary BD +52 °2009, based on Reticon observations, are presented. The velocity measures are based on fitting theoretical profiles, generated by a physical model of the binary, to the observed cross-correlation function (ccf). Such profiles match this function very well, much better in fact than Gaussian profiles, which are generally used. Measuring the ccf’s with Gaussian profiles yields the following results: mp sin3i = 2.55 ± 0.05m⊙, ms sin3i = 1.14 ± 0.03m⊙, (ap + as) sin i = 7.34 ± 0.05R⊙, and mp/ms = 2.23 ± 0.05. However, measuring the ccf’s with theoretical profiles yields a mass ratio of 2.33 and following results: mp sin3i = 2.84 ± 0.05m⊙, ms sin3i = 1.22 ± 0.03m⊙, (ap + as) sin i = 7.56 ± 0.05R⊙. The system has a semi-detached configuration. By combining the solution of a previously published light curve with the spectroscopic orbit, one can obtain the following physical parameters: mp = 2.99m⊙, ms3 = 1.28m⊙, < Tp >= 9600K, < Ts >= 5400K, < Rp >= 2.35R⊙, < Rs >= 2.12R⊙. The system consists of an A0 primary and a G2 secondary.

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