Results 111 to 120 of about 44,286,818 (153)

The Multiple Scales Method, Homoclinic Bifurcation and Melnikov's Method for Autonomous Systems

International Journal of Bifurcation and Chaos, 1998
Melnikov's method is a well-established technique for detecting homoclinic bifurcation of perturbed autonomous or forced systems. This method uses a regular perturbation expansion in terms of a small parameter in the system. Whilst the approach correctly estimates the parameter values for the bifurcation and transverse intersections of separatrices ...
Peter Smith
openaire   +2 more sources

On Melnikov's method in the study of chaotic motions of gyrostat

International Journal of Control, 2002
The homoclinic solutions of the attitude motion of a gyrostat with wheels along its principal axes are formulated using the procedure developed by Wittenburg. The generic Melnikov function for the attitude motion of a gyrostat subject to small non-linear damping torques and small periodic torques is derived.
Jinlu Kuang, Soonhie Tan, A. Y. T. Leung
openaire   +2 more sources

High order Melnikov method: Pendulums

Journal of Differential Equations, 2022
This paper is concerned with the computation of the second order Melnikov function for periodically perturbed pendulum equations given by \[ \frac{dx}{dt}=y,\qquad \frac{dy}{dt}=-\sin x +\varepsilon\cos^2(x/2)\cdot P(t), \] where \(P(t)\) is a periodic function in \(t\) and \(\varepsilon\) is a small parameter.
Oksasoglu, Ali, Wang, Qiudong
openaire   +1 more source

Equivalence of the Melnikov Function Method and the Averaging Method

Qualitative Theory of Dynamical Systems, 2015
In this paper, the authors study the problem of equivalence between the Melnikov method and the averaging method for studying the number of limit cycles which can bifurcate from the period annulus of planar analytic differential systems.
Maoan Han, Valery G. Romanovski, Xiang Zhang   +2 more
openaire   +1 more source

Higher-order Melnikov method

Applied Mathematics and Mechanics, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo You-zhong, Liu Zeng-rong, Jiang Xia-mei, Han Zhi-bin   +3 more
openaire   +1 more source

Melnikov method for parabolic orbits

NoDEA : Nonlinear Differential Equations and Applications, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Casasayas, Josefina, Faisca, Patrícia, Nunes, Ana   +2 more
openaire   +2 more sources

EXPONENTIAL DICHOTOMIES, HOMOCLINIC ORBITS AND METHODS OF MELNIKOV

Acta Mathematica Scientia, 1996
The main goal of this paper is to investigate the existence of transversal homoclinic orbits of the perturbed equation \[ dx/dt= g(x)+ \varepsilon h(t,x,\varepsilon).\tag{\(*\)} \] The authors construct a Melnikov-type function which yields transversal homoclinic orbits also when the perturbation does not depend on \(t\).
Zeng, Weiyao, Qian, Xiangzheng, Wang, Zhicheng   +2 more
openaire   +2 more sources

High order Melnikov method: Theory and application

Journal of Differential Equations, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Fengjuan, Q. D. Wang, Qiudong
openaire   +2 more sources

On the Equivalence of the Melnikov Functions Method and the Averaging Method

Qualitative Theory of Dynamical Systems, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

A practical use of the Melnikov homoclinic method

Journal of Mathematical Physics, 2009
Using cutoff functions and periodic extensions, we prove that the Melnikov homoclinic method gives a criterium to show that for a finite time interval [−T,T], with T arbitrarily large, the perturbed system is conjugated to a chaotic one for quite general classes of perturbation functions.
Castilho, César, Marchesin, Marcelo
openaire   +1 more source