Results 51 to 60 of about 7,901 (195)

Best difference equation approximation to Duffing's equation [PDF]

The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1982
AbstractDuffing's differential equation in its simplest form can be approximated by a variety of difference equations. It is shown how to choose a ‘best’ difference equation in the sense that the solutions of this difference equation are successive discrete exact values of the solution of the differential equation.
openaire   +2 more sources

On a Duffing-type oscillator differential equation on the transition to chaos with fractional q-derivatives

Journal of Inequalities and Applications
In this paper, by applying fractional quantum calculus, we study a nonlinear Duffing-type equation with three sequential fractional q-derivatives. We prove the existence and uniqueness results by using standard fixed-point theorems (Banach and Schaefer ...
Mohamed Houas, Mohammad Esmael Samei, Shyam Sundar Santra, Jehad Alzabut   +3 more
doaj   +1 more source

Lagrange stability for a class of impulsive Duffing equation with low regularity

Electronic Journal of Qualitative Theory of Differential Equations
We discuss the Lagrange stability for a class of impulsive Duffing equation with time-dependent polynomial potentials. More precisely, we prove that under suitable impulses, all the solutions of the impulsive Duffing equation (with low regularity in time)
Xiaolong He, Yueqin Sun, Jianhua Shen
doaj   +1 more source

Wada property in systems with delay

, 2016
Delay differential equations take into account the transmission time of the information. These delayed signals may turn a predictable system into chaotic, with the usual fractalization of the phase space.
Daza, Alvar, Sanjuán, Miguel A. F., Wagemakers, Alexandre   +2 more
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Haar Wavelet Operational Matrix Method for Fractional Oscillation Equations

International Journal of Mathematics and Mathematical Sciences, 2014
We utilized the Haar wavelet operational matrix method for fractional order nonlinear oscillation equations and find the solutions of fractional order force-free and forced Duffing-Van der Pol oscillator and higher order fractional Duffing equation on ...
Umer Saeed, Mujeeb ur Rehman
doaj   +1 more source

The dissipative quantum Duffing oscillator: a comparison of Floquet-based approaches

, 2010
We study the dissipative quantum Duffing oscillator in the deep quantum regime with two different approaches: The first is based on the exact Floquet states of the linear oscillator and the nonlinearity is treated perturbatively.
Almog, Alridge, Aravind, Blum, Blümel, Blümel, Breuer, Caldeira, Carmen Vierheilig, Certain, Certain, Cohen-Tannoudji, Dykman, Etaki, Floquet, Grifoni, Husimi, Jordan, Katz, Katz, Kirtman, Kohler, Kohler, Lee, Louisell, Metcalfe, Milena Grifoni, Nakano, Nation, Nayfeh, Nolting, Peano, Peano, Peano, Perelomov, Picot, Rigo, Sambe, Serban, Serban, Shavitt, Shirley, Siddiqi, Siddiqi, Stone, Tittonen, Vierheilig   +46 more
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Tunable Broadband Transparency of Macroscopic Quantum Superconducting Metamaterials [PDF]

, 2015
Narrow-band invisibility in an otherwise opaque medium has been achieved by electromagnetically induced transparency (EIT) in atomic systems. The quantum EIT behaviour can be classically mimicked by specially engineered metamaterials via carefully ...
Anlage, Steven. M., Mukhanov, Oleg, Trepanier, Melissa, Zhang, Daimeng   +3 more
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EXACT SOLUTIONS TO CUBIC DUFFING EQUATION FOR A NONLINEAR ELECTRICAL CIRCUIT

Visión Electrónica, 2014
This work provides an exact solution to a cubic Duffing oscillator equation with initial conditions and bounded periodic solutions. This solution is expressed in terms of the Jacobi elliptic function (cn).
Álvaro H. Salas S., Jairo E. Castillo H
doaj  

Lagrange Stability for Duffing-Type Equations

Journal of Differential Equations, 2000
The boundedness of solutions (Lagrange stability) to a generalized Duffing equation of the form \[ \frac{d^2 x}{dt^2} + x^{2n+1} + \sum_{j=0}^{2n} p_j (t)x^j = 0, \quad n\geq 1, \tag{1} \] with \(p_j (t+1)= p(t) \) is considered. The conditions for the \(p_j's\) which lead to the boundedness of the solutions to (1) were investigated by many authors ...
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Locally Exact Integrators for the Duffing Equation

Mathematics, 2020
A numerical scheme is said to be locally exact if after linearization (around any point) it becomes exact. In this paper, we begin with a short review on exact and locally exact integrators for ordinary differential equations.
Jan L. Cieśliński, Artur Kobus
doaj   +1 more source