scholarly journals Subharmonic orbits in an anharmonic oscillator

1997 ◽  
Vol 38 (3) ◽  
pp. 307-315 ◽  
Author(s):  
J. R. Christie ◽  
K. Gopalsamy ◽  
M. P. Panizza
Keyword(s):  
Differential Equations ◽  
Autonomous System ◽  
Anharmonic Oscillator ◽  
Dynamical Behaviour ◽  
Sufficient Condition ◽  
One Dimensional ◽  
Perturbed System ◽  
Melnikov Theory ◽  
The One ◽  
Subharmonic Orbits

AbstractIn a recent paper, Christie and Gopalsamy [2] used Melnikov's method to establish a sufficient condition for the existence of chaotic behaviour, in the sense of Smale, in a particular time-periodically perturbed planar autonomous system of ordinary differential equations. They then concluded with an application to the dynamics of a one-dimensional anharmonic oscillator. In this paper, the same system is considered and a condition for the existence of subharmonic orbits in the perturbed system is deduced, using the subharmonic Melnikov theory. Finally, an application is given to the dynamical behaviour of the one-dimensional anharmonic oscillator system.

scholarly journals Chaos in an anharmonic oscillator

1995 ◽  
Vol 37 (2) ◽  
pp. 186-207 ◽  
Author(s):  
J. R. Christie ◽  
K. Gopalsamy
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Autonomous System ◽  
Anharmonic Oscillator ◽  
Homoclinic Orbits ◽  
Chaotic Behaviour ◽  
Differential Systems ◽  
Melnikov's Method ◽  
One Dimensional ◽  
Melnikov’S Method

AbstractUsing Melnikov's method, the existence of chaotic behaviour in the sense of Smale in a particular time-periodically perturbed planar autonomous system of ordinary differential equations is established. Examples of planar autonomous differential systems with homoclinic orbits are provided, and an application to the dynamics of a one-dimensional anharmonic oscillator is given.

A limit theorem for certain disordered random systems

1994 ◽  
Vol 26 (04) ◽  
pp. 1022-1043 ◽  
Author(s):  
Xinhong Ding
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Limit Theorem ◽  
Random Systems ◽  
Joint Probability ◽  
Dynamical Behaviour ◽  
One Dimensional ◽  
Linear Stochastic Differential Equation ◽  
The One ◽  
Image Position

Many disordered random systems in applications can be described by N randomly coupled Ito stochastic differential equations in : where is a sequence of independent copies of the one-dimensional Brownian motion W and ( is a sequence of independent copies of the ℝ p -valued random vector ξ. We show that under suitable conditions on the functions b, σ, K and Φ the dynamical behaviour of this system in the N → (limit can be described by the non-linear stochastic differential equation where P(t, dx dy) is the joint probability law of ξ and X(t).

scholarly journals Algebraic approach for the one-dimensional Dirac–Dunkl oscillator

2020 ◽  
Vol 35 (31) ◽  
pp. 2050255
Author(s):  
D. Ojeda-Guillén ◽  
R. D. Mota ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Energy Spectrum ◽  
Irreducible Representation ◽  
Differential Equations ◽  
Representation Theory ◽  
Algebraic Approach ◽  
The Other ◽  
One Dimensional ◽  
The One

We extend the (1 + 1)-dimensional Dirac–Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac–Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate su(1, 1) algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the su(1, 1) irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.

Comparison Theorem for any Solutions of Backward Stochastic Differential Equations and its Application

2012 ◽  
Vol 524-527 ◽  
pp. 3801-3804
Author(s):  
Shi Yu Li ◽  
Wu Jun Gao ◽  
Jin Hui Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Equations ◽  
Local Martingale ◽  
One Dimensional ◽  
Lipschitz Continuous ◽  
The One ◽  
Uniformly Lipschitz

ƒIn this paper, we study the one-dimensional backward stochastic equations driven by continuous local martingale. We establish a generalized the comparison theorem for any solutions where the coefficient is uniformly Lipschitz continuous in z and is equi-continuous in y.

Determination of Optimum Profile of One-Dimensional Cooling Fins

1983 ◽  
Vol 105 (3) ◽  
pp. 317-320 ◽  
Author(s):  
S. K. Hati ◽  
S. S. Rao
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Minimum Principle ◽  
Problem Formulation ◽  
One Dimensional ◽  
A New Technique ◽  
The One ◽  
Optimum Profile

The optimum design of an one-dimensional cooling fin is considered by including all modes of heat transfer in the problem formulation. The minimum principle of Pontryagin is applied to determine the optimum profile. A new technique is used to solve the reduced differential equations with split boundary conditions. The optimum profile found is compared with the one obtained by considering only conduction and convection.

scholarly journals The existence of three positive solutions to integral type BVPs for singular second ODEs with one-dimensional p-Laplacian

2011 ◽  
Vol 27 (2) ◽  
pp. 239-248
Author(s):  
YUJI LIU ◽  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Type ◽  
Singular Differential Equations ◽  
One Dimensional ◽  
Type Boundary ◽  
The One

This paper is concerned with the integral type boundary value problems of the second order singular differential equations with one-dimensional p-Laplacian. Sufficient conditions to guarantee the existence of at least three positive solutions are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensional p-Laplacian term [ρ(t)Φ(x 0 (t))]0 involved with the function ρ, which makes the solutions un-concave. Furthermore, f, g, h and ρ may be singular at t = 0 or t = 1.

Proposed Use of the One-Dimensional Two-Fluid Model With Momentum Flux Parameters

2000 ◽  
Author(s):  
Jin Ho Song ◽  
H. D. Kim
Keyword(s):  
Differential Equations ◽  
Void Fraction ◽  
Momentum Flux ◽  
Fluid Model ◽  
Sufficient Conditions ◽  
Wave Number ◽  
One Dimensional ◽  
Two Fluid Model ◽  
The One ◽  
Two Fluid

Abstract The dynamic character of a system of the governing differential equations for the one-dimensional two-fluid model, where the appropriate momentum flux parameters are employed to consider the velocity and void fraction distribution in a flow channel, is analyzed. In response to a perturbation in the form of a traveling wave, a linear stability analysis is performed for the governing differential equations. The analytical expression for the growth factor as a function of wave number, void fraction, drag coefficient, and relative velocity is derived. It provides the necessary and sufficient conditions for the stability of the one-dimensional two-fluid model in terms of momentum flux parameters. It is analytically shown that the one-dimensional two-fluid model is mathematically well posed by use of appropriate momentum flux parameters, while the conventional two-fluid model makes the system unconditionally unstable. It is suggested that the velocity and void distributions should be properly accounted for in the one-dimensional two-fluid model by use of momentum flux parameters.

On the stability of some solutions of the Stefan problem

1991 ◽  
Vol 2 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Riccardo Ricci ◽  
Xie Weiqing
Keyword(s):  
Stefan Problem ◽  
Travelling Wave ◽  
Sufficient Condition ◽  
Travelling Wave Solutions ◽  
Necessary And Sufficient Condition ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Necessary And Sufficient ◽  
Travelling Wave Front

We investigate the stability of travelling wave solutions of the one-dimensional under-cooled Stefan problem. We find a necessary and sufficient condition on the initial datum under which the free boundary is asymptotic to a travelling wave front. The method applies also to other types of solutions.

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