scholarly journals On asymptotically periodic-like motions in flows

2018 ◽  
Vol 17 (1) ◽  
pp. 45-57
Author(s):  
Karol Gryszka
Keyword(s):  
Lyapunov Stability ◽  
Asymptotically Periodic ◽  
Asymptotic Periodicity

Abstract We study three properties associated to the recurrence of orbits in flows: asymptotic periodicity, positive asymptotic periodicity and G-asymptotic periodicity. We determine which implications between these notions hold and which do not. We also show how these notions are related to Lyapunov stability.

scholarly journals Asymptotic periodicity in outer billiards with contraction

2018 ◽  
Vol 40 (2) ◽  
pp. 402-417
Author(s):  
JOSÉ PEDRO GAIVÃO
Keyword(s):  
Finite Number ◽  
Periodic Orbits ◽  
Convex Polygon ◽  
Asymptotically Periodic ◽  
Outer Billiards ◽  
Asymptotic Periodicity

We show that for almost every $(P,\unicode[STIX]{x1D706})$, where $P$ is a convex polygon and $\unicode[STIX]{x1D706}\in (0,1)$, the corresponding outer billiard about $P$ with contraction $\unicode[STIX]{x1D706}$ is asymptotically periodic, i.e., has a finite number of periodic orbits and every orbit is attracted to one of them.

scholarly journals Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhinan Xia
Keyword(s):  
Fixed Point ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Exponential Dichotomy ◽  
Second Order ◽  
Order Difference ◽  
Asymptotically Periodic ◽  
Asymptotic Periodicity ◽  
Asymptotically Periodic Solution ◽  
Composition Theorem

We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.

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.

Fixed-time tracking control for two-link rigid manipulator based on disturbance observer

2021 ◽  
pp. 014233122098363
Author(s):  
Heli Gao ◽  
Mou Chen
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Tracking Control ◽  
Disturbance Observer ◽  
Inverse Dynamics ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Extended State

This paper studies the fixed-time disturbance estimate and tracking control for two-link manipulators subjected to external disturbance. A fixed-time extended-state disturbance observer (FxTESDO) is proposed by improving the extended state observer. Also, a fixed-time inverse dynamics tracking control (FxTIDTC) scheme based on the FxTESDO is given for two-link manipulators. The fixed-time convergence of the FxTESDO and FxTIDTC is proved by the Lyapunov stability theory and with the aid of the bi-limit homogeneous technique. Numerical simulations are employed to illustrate the effectiveness of the proposed FxTIDTC.

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.

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

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