Add to ORKGWe establish an asymptotic lower bound for the minimum excitation needed to cause instability for the damped Mathieu equation. The methods used are Floquet theory and Lyapunov-Schmidt, and we use a fact about the width of the instability interval for the undamped Mathieu equation. Our results are compared with published numerical data
Parametric excitation is epitomized by the Mathieu equation, x''+(d + e cos t)x = 0, which involves ...
In the following we consider a 2-dimensional system of ODEs containing quasiperiodic terms. The syst...
We study the asymptotics for the lengths of the instability tongues L_N(q) of Hill equations that ar...
We establish an asymptotic lower bound for the minimum excitation needed to cause instability for th...
An improved stability criterion is derived for the damped Mathieu equation using periodic Lyapunov f...
The form of the fundamental set of solutions of the damped Mathieu equation is determined by Floquet...
The Mathieu equation $X^n$ +(a–2q cos2t)x=0 has been studied in great detail since its discovery in...
The classic linear Mathieu equation is one of the archetypical differential equations which has been...
Various phenomena in science, physics, and engineering result in the Mathieu equation with cubic non...
A theoretical analysis is presented of the response of a lightly and nonlinearly damped mass–spring ...
AbstractThe paper presents the results of a homogeneous Mathieu equation studies. Mathieu equation s...
We have investigated the solution of the generalized Mathieu equation. With the aid of diagrams Stra...
This paper analyzes the stochastic stability of a damped Mathieu oscillator subjected to a parametri...
The purpose of the article is to present new solutions of the Mathieu Duffing equation in the zone o...
In a recent publication [H. Tasso and G. N. Throumoulopoulos, Phys. Lett. A 271, 413 (2000)] on Lyap...
Parametric excitation is epitomized by the Mathieu equation, x''+(d + e cos t)x = 0, which involves ...
In the following we consider a 2-dimensional system of ODEs containing quasiperiodic terms. The syst...
We study the asymptotics for the lengths of the instability tongues L_N(q) of Hill equations that ar...
We establish an asymptotic lower bound for the minimum excitation needed to cause instability for th...
An improved stability criterion is derived for the damped Mathieu equation using periodic Lyapunov f...
The form of the fundamental set of solutions of the damped Mathieu equation is determined by Floquet...
The Mathieu equation $X^n$ +(a–2q cos2t)x=0 has been studied in great detail since its discovery in...
The classic linear Mathieu equation is one of the archetypical differential equations which has been...
Various phenomena in science, physics, and engineering result in the Mathieu equation with cubic non...
A theoretical analysis is presented of the response of a lightly and nonlinearly damped mass–spring ...
AbstractThe paper presents the results of a homogeneous Mathieu equation studies. Mathieu equation s...
We have investigated the solution of the generalized Mathieu equation. With the aid of diagrams Stra...
This paper analyzes the stochastic stability of a damped Mathieu oscillator subjected to a parametri...
The purpose of the article is to present new solutions of the Mathieu Duffing equation in the zone o...
In a recent publication [H. Tasso and G. N. Throumoulopoulos, Phys. Lett. A 271, 413 (2000)] on Lyap...
Parametric excitation is epitomized by the Mathieu equation, x''+(d + e cos t)x = 0, which involves ...
In the following we consider a 2-dimensional system of ODEs containing quasiperiodic terms. The syst...
We study the asymptotics for the lengths of the instability tongues L_N(q) of Hill equations that ar...