scholarly journals Twist Periodic Solutions in the Relativistic Driven Harmonic Oscillator

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Daniel Núñez ◽  
Andrés Rivera
Keyword(s):  
Periodic Solution ◽  
Harmonic Oscillator ◽  
Periodic Solutions ◽  
Relativistic Effects ◽  
Stable Periodic Solution ◽  
One Dimensional ◽  
Stable Periodic ◽  
The One ◽  
Hill’S Equations ◽  
Twist Theorem

We study the one-dimensional forced harmonic oscillator with relativistic effects. Under some conditions of the parameters, the existence of a unique stable periodic solution is proved which is of twist type. The results depend on a Twist Theorem for nonlinear Hill’s equations which is established and proved here.

scholarly journals Periodic Solutions of a System of Delay Differential Equations for a Small Delay

2002 ◽  
Vol 7 (2) ◽  
pp. 295
Author(s):  
Adu A.M. Wasike ◽  
Wandera Ogana
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Original System ◽  
System Of Equations ◽  
Asymptotically Stable ◽  
Stable Periodic Solution ◽  
Stable Periodic ◽  
Delay Differential

We prove the existence of an asymptotically stable periodic solution of a system of delay differential equations with a small time delay t > 0. To achieve this, we transform the system of equations into a system of perturbed ordinary differential equations and then use perturbation results to show the existence of an asymptotically stable periodic solution. This approach is contingent on the fact that the system of equations with t = 0 has a stable limit cycle. We also provide a comparative study of the solutions of the original system and the perturbed system.  This comparison lays the ground for proving the existence of periodic solutions of the original system by Schauder's fixed point theorem.   

Analytical and Numerical Investigations of Stable Periodic Solutions of the Impacting Oscillator With a Moving Base and Two Fenders

2017 ◽  
Vol 12 (6) ◽  
Author(s):  
Barbara Blazejczyk-Okolewska ◽  
Krzysztof Czolczynski ◽  
Andrzej Okolewski
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Analytical Method ◽  
Equations Of Motion ◽  
Moving Frame ◽  
Stable Periodic Solution ◽  
Bifurcation Diagrams ◽  
Numerical Investigations ◽  
Moving Base ◽  
Stable Periodic

A vibrating system with impacts, which can be applied to model the cantilever beam with a mass at its end and two-sided impacts against a harmonically moving frame, is investigated. The objective of this study is to determine in which regions of parameters characterizing system, the motion of the oscillator is periodic and stable. An analytical method to obtain stable periodic solutions to the equations of motion on the basis of Peterka's approach is presented. The results of analytical investigations have been compared to the results of numerical simulations. The ranges of stable periodic solutions determined analytically and numerically with bifurcation diagrams of spectra of Lyapunov exponents show a very good conformity. The locations of stable periodic solution regions of the system with a movable frame and two-sided impacts differ substantially from the locations of stable periodic solution regions for the system: (i) with a movable frame and one-sided impacts and (ii) with an immovable frame and two-sided impacts.

scholarly journals Permanence and Periodic Solution of Predator-Prey System with Holling Type Functional Response and Impulses

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Weibing Wang ◽  
Jianhua Shen ◽  
Juan J. Nieto
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Effect ◽  
Two Dimensional ◽  
Stable Periodic Solution ◽  
Predator Prey ◽  
Prey System ◽  
Stable Periodic ◽  
Holling Type Functional Response

We considered a nonautonomous two dimensional predator-prey system with impulsive effect. Conditions for the permanence of the system and for the existence of a unique stable periodic solution are obtained.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

scholarly journals Periodic solutions for the one-dimensional fractional Laplacian

2019 ◽  
Vol 267 (9) ◽  
pp. 5258-5289 ◽  
Author(s):  
B. Barrios ◽  
J. García-Melián ◽  
A. Quaas
Keyword(s):  
Periodic Solutions ◽  
Fractional Laplacian ◽  
One Dimensional ◽  
The One

Quantum mechanics on (anti)-de Sitter background II: Ramsauer–Townsend effect and WKB method

2018 ◽  
Vol 33 (26) ◽  
pp. 1850150 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Harmonic Oscillator ◽  
Wkb Method ◽  
De Sitter ◽  
Quantum Harmonic Oscillator ◽  
One Dimensional ◽  
Sitter Background ◽  
The One

Based on the one-dimensional quantum mechanics on (anti)-de Sitter background [W. S. Chung and H. Hassanabadi, Mod. Phys. Lett. A 32, 26 (2107)], we discuss the Ramsauer–Townsend effect. We also formulate the WKB method for the quantum mechanics on (anti)-de Sitter background to discuss the energy level of the quantum harmonic oscillator and quantum bouncer.

ON THE INFLUENCE OF THE RESONANT FREQUENCIES RATIO ON A STABLE PERIODIC SOLUTION OF TWO IMPACTING OSCILLATORS

2006 ◽  
Vol 16 (12) ◽  
pp. 3707-3715 ◽  
Author(s):  
KRZYSZTOF CZOLCZYNSKI ◽  
TOMASZ KAPITANIAK
Keyword(s):  
Periodic Solution ◽  
Periodic Motion ◽  
Stable Periodic Solution ◽  
Resonant Frequencies ◽  
Stable Periodic

A system that consists of two impacting oscillators with damping has been considered in this paper. The goal of the studies was to determine the relation between the values of resonant frequencies of the oscillators and the existence of their stable periodic motion. This paper indicates various origins of the periodicity of motion and offers a some advice to the designers of systems with impacts. Especially, the results of the considerations point out some potentially dangerous consequences of the improper value of the resonant frequencies ratio.

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