Symmetry Properties in the Symmetry-Breaking of Nonsmooth Dynamical Systems

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
Alessio Ageno ◽  
Anna Sinopoli
Keyword(s):  
Group Theory ◽  
Stability Analysis ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Simply Supported ◽  
Symmetry Properties ◽  
Existence Conditions ◽  
Asymmetric Responses ◽  
The Stability ◽  
Nonsmooth Dynamical Systems

In this paper, the block simply supported on a harmonically moving ground is assumed as a system well representing a typical nonsmooth dynamical behavior. The aim of the work is to carry out the existence conditions of asymmetric responses; an analysis that comes first in any stability investigation. By using simple definitions belonging to the symmetry group theory, it is possible to completely clarify the relationships between the various initial conditions that allow simple asymmetric responses, and to develop tools, which will be very useful in the stability analysis of more complex asymmetric responses.

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.

A GLOBAL PERIOD-1 MOTION OF A PERIODICALLY EXCITED, PIECEWISE-LINEAR SYSTEM

2005 ◽  
Vol 15 (06) ◽  
pp. 1945-1957 ◽  
Author(s):  
SANTHOSH MENON ◽  
ALBERT C. J. LUO
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Piecewise Linear ◽  
Dynamical Behavior ◽  
Analytical Prediction ◽  
Algebraic Equations ◽  
Piecewise Linear System ◽  
Nonlinear Algebraic Equations ◽  
The Stability ◽  
Nonsmooth Dynamical Systems

The period-1 motion of a piecewise-linear system under a periodic excitation is predicted analytically through the Poincaré mapping and the corresponding mapping sections formed by the switch planes pertaining to the two constraints. The mapping relationship generates a set of nonlinear algebraic equations from which the period-1 motion is determined analytically. The stability and bifurcation of the period-1 motion are determined, and numerical simulations are carried out for confirmation of the analytical prediction of period-1 motion. An unsymmetrical stable period-1 motion is observed. This investigation helps us understand the dynamical behavior of period-1 motion in the piecewise-linear system and more efficiently obtain other periodic motions and chaos through numerical simulations. The similar methodology presented in this paper can be used for other nonsmooth dynamical systems.

Dynamics and Stability of a Nonlinear Brake Model

2001 ◽  
Author(s):  
Jörg Wauer ◽  
Jürgen Heilig
Keyword(s):  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Nonlinear Model ◽  
Numerical Evaluation ◽  
Critical Speed ◽  
Initial Conditions ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Pad ◽  
The Stability

Abstract The dynamics of a nonlinear car disc brake model is investigated and compared with a simplified linear model. The rotating brake disc is approximated by a rotating ring. The brake pad is modeled as a point mass which is in contact with the rotating ring and visco-elastically suspended in axial and circumferential direction. The stability analysis for the nonlinear model is performed by a numerical evaluation of the top Lyapunov-exponent. Several parameter studies for the nonlinear model are discussed. It is shown that dynamic instabilities of the nonlinear model are estimated at subcritical rotating speeds lower than 10% of the critical speed. Further, the sensitivity of the nonlinear model to the initial conditions and the stiffness ratios is demonstrated.

Atomic motion and dipole–dipole effects on the stability of atom–atom entanglement in Markovian/non-Markovian reservoir

2019 ◽  
Vol 34 (10) ◽  
pp. 1950077 ◽  
Author(s):  
S. Golkar ◽  
M. K. Tavassoly
Keyword(s):  
Weak Coupling ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Dipole Interaction ◽  
Zero Temperature ◽  
Entanglement Dynamics ◽  
Entanglement Protection ◽  
Initial States ◽  
The Stability ◽  
Suitable Measure

In this paper, we consider the entanglement dynamics of two identical qubits (two-level atoms) accompanied by dipole–dipole interaction within a common reservoir in the strong and weak coupling regimes. We suppose that the qubits move in the reservoir which is at zero temperature. Using the time-dependent Schrödinger equation, the state vector of the qubits-reservoir system is obtained by which we can evaluate the concurrence as a suitable measure of entanglement between the two qubits. The results show that by choosing special initial conditions for the qubits, a different dynamical behavior of entanglement is visible in such a way that entanglement protection occurs. Also, we find that the qubit motion in the absence of dipole–dipole interaction leads to preservation or at least more slowly decay of entanglement. However, in the presence of dipole–dipole interaction with the movement of qubits, different results can be observed which depend on the initial states of the qubits, i.e. entanglement may or may not be protected.

scholarly journals Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation

2015 ◽  
pp. 196-204
Author(s):  
Г.В. Кривовичев ◽  
С.А. Михеев
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Linear Approximation ◽  
Lattice Boltzmann ◽  
Initial Conditions ◽  
Order Approximation ◽  
Stability Study ◽  
High Order Approximation ◽  
Spatial Variables ◽  
The Stability

Исследуется устойчивость трехслойных конечно-разностных решеточных схем Больцмана третьего и четвертого порядков аппроксимации по пространственным переменным. Проводится анализ устойчивости по начальным условиям с использованием линейного приближения. Для исследования используется метод Неймана. Показано, что устойчивость схем можно улучшить за счет аппроксимации конвективных членов во внутренних узлах сеточного шаблона. В этом случае удается получать большие по площади области устойчивости, чем при аппроксимации в граничных узлах шаблона. The stability of three-level finite-difference-based lattice Boltzmann schemes of third and fourth orders of approximation with respect to spatial variables is studied. The stability analysis with respect to initial conditions is performed on the basis of a linear approximation. These studies are based on the Neumann method. It is shown that the stability of the schemes can be improved by the approximation convective terms in internal nodes of the grid stencils in use. In this case the stability domains are larger compared to the case of approximation in boundary nodes.

scholarly journals Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Agus Suryanto ◽  
Isnani Darti ◽  
Syaiful Anam
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Local Stability ◽  
Allee Effect ◽  
Dynamical Behavior ◽  
Continuous Model ◽  
Positivity Of Solutions ◽  
Existence Conditions ◽  
Dynamical Properties

We analyze the dynamics of a fractional order modified Leslie-Gower model with Beddington-DeAngelis functional response and additive Allee effect by means of local stability. In this respect, all possible equilibria and their existence conditions are determined and their stability properties are established. We also construct nonstandard numerical schemes based on Grünwald-Letnikov approximation. The constructed scheme is explicit and maintains the positivity of solutions. Using this scheme, we perform some numerical simulations to illustrate the dynamical behavior of the model. It is noticed that the nonstandard Grünwald-Letnikov scheme preserves the dynamical properties of the continuous model, while the classical scheme may fail to maintain those dynamical properties.

scholarly journals Stability of Vertically Traveling, Pre-tensioned, Heavy Cables

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
Abhinav Ravindra Dehadrai ◽  
Ishan Sharma ◽  
Shakti S. Gupta
Keyword(s):  
Stability Analysis ◽  
Governing Equation ◽  
Initial Conditions ◽  
Slenderness Ratio ◽  
Equation Of Motion ◽  
Rate Of Change ◽  
Bending Rigidity ◽  
Stable Regime ◽  
Varying Coefficients ◽  
The Stability

We study the stability of a pre-tensioned, heavy cable traveling vertically against gravity at a constant speed. The cable is modeled as a slender beam incorporating rotary inertia. Gravity modifies the tension along the traveling cable and introduces spatially varying coefficients in the equation of motion, thereby precluding an analytical solution. The onset of instability is determined by employing both the Galerkin method with sine modes and finite element (FE) analysis to compute the eigenvalues associated with the governing equation of motion. A spectral stability analysis is necessary for traveling cables where an energy stability analysis is not comprehensive, because of the presence of gyroscopic terms in the governing equation. Consistency of the solution is checked by direct time integration of the governing equation of motion with specified initial conditions. In the stable regime of operations, the rate of change of total energy of the system is found to oscillate with bounded amplitude indicating that the system, although stable, is nonconservative. A comprehensive stability analysis is carried out in the parameter space of traveling speed, pre-tension, bending rigidity, external damping, and the slenderness ratio of the cable. We conclude that pre-tension, bending rigidity, external damping, and slenderness ratio enhance the stability of the traveling cable while gravity destabilizes the cable.

scholarly journals On the Global Stability Analysis of Corona Virus Disease (COVID-19) Mathematical Model

2021 ◽  
pp. 81-87
Author(s):  
William Atokolo ◽  
Achonu Omale Joseph ◽  
Rose Veronica Paul ◽  
Abdul Sunday ◽  
Thomas Ugbojoide Onoja
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Initial Conditions ◽  
Virus Disease ◽  
Disease Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Global Stability Analysis ◽  
Corona Virus ◽  
The Stability

In this present work, we investigated the Global Stability Analysis of Corona virus disease model formulated by Atokolo et al in [11]. The COVID‑19 pandemic, also known as the coronavirus pandemic, is an ongoing pandemic that is ravaging the whole world. By constructing a Lyapunov function, we investigated the stability of the model Endemic Equilibrium state to be globally asymptotically stable. This results epidemiologically implies that the COVID-19 will invade the population in respective of the initial conditions (population) considered.

Stability Analysis of High-Performance Drones With Suspended Payloads

2019 ◽  
Author(s):  
Samantha Hoang ◽  
Yifeng Liu ◽  
Alberto Aliseda ◽  
I. Y. Shen
Keyword(s):  
Stability Analysis ◽  
Nonlinear System ◽  
High Performance ◽  
Initial Conditions ◽  
Wind Disturbance ◽  
External Disturbances ◽  
Nonlinear Simulations ◽  
Linearized System ◽  
Payload Mass ◽  
The Stability

Abstract This paper studies the stability of a system consisting of a drone with a heavy payload through both linear stability analysis and nonlinear simulations. The stability is studied with respect to two payload parameters: the length of the arm the payload is suspended from and the mass of the payload. Linearizing the drone-payload system around vertical flight results in a linearized system that is marginally stable with five negative, real eigenvalues and seven zero-eigenvalues. The presence of seven zero-eigenvalues makes it difficult to predict the stability of the nonlinear system so nonlinear simulations are completed to understand how the drone-payload system reacts to external disturbances. To directly study the severity of the nonlinear system’s instability, the system is subjected to an initial, one-second wind disturbance that induces different initial conditions on the system. The results of the nonlinear simulations indicate that the presence of a suspended payload will always cause the drone-payload system to be unstable. Both an increase in the length of the payload arm and the payload mass will individually increase the deviation of the system from the expected path.

scholarly journals Evolution of an Exponential Polynomial Family of Discrete Dynamical Systems

2019 ◽  
Vol 24 (1) ◽  
pp. 13 ◽  
Author(s):  
Francisco Solis
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Dynamical Systems ◽  
Dynamical Behavior ◽  
Discrete Dynamical Systems ◽  
Exponential Polynomial ◽  
Linear Dynamical System ◽  
The Stability ◽  
Polynomial Family ◽  
Complex Dynamical Behavior

In this paper, we introduce and analyze a family of exponential polynomial discrete dynamical systems that can be considered as functional perturbations of a linear dynamical system. The stability analysis of equilibria of this family is performed by considering three different parametric scenarios, from which we show the intricate and complex dynamical behavior of their orbits.

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