Results 1 to 10 of about 27,933 (207)
On the Melnikov function [PDF]
ریاضی و جامعه, 2023 In this article, we have tried to introduce one of the most important topics in the subject of dynamical systems, namely the Melnikov function, in simple language.
Majid Karimi Amaleh
doaj +2 more sources
A note on the Melnikov function [PDF]
Vietnam Journal of Mechanics, 2007 With one (Poincaré section) parameter and a particular motion law (that associated to certain determined point of horno-heteroclinic orbits), the usual form of the Melnikov function seems to be not convenient for certain problems.
Nguyen Van Dinh
doaj +2 more sources
Experimental measurement of the Melnikov function [PDF]
Physics of Fluids, 2015 International audienceWe study the transport properties of a genuine two-dimensional flow with a large mean velocity perturbed periodically in time by means of an original experimental technique. The flow, generated by the co-rotation of two cylinders is
Huck, Peter +3 more
core +4 more sources
On the number of zeros of Melnikov functions [PDF]
Annales de la Faculté des sciences de Toulouse : Mathématiques, 2010 We provide an effective uniform upper bond for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field.
Benditkis, Sergey, Novikov, Dmitry
core +5 more sources
Some remarks on the Melnikov function
Electronic Journal of Differential Equations, 2002 We study the Melnikov function associated with a periodic perturbation of a differential equation having a homoclinic orbit. Our main interest is the characterization of perturbations that give rise to vanishing or non-vanishing of the Melnikov function.
Flaviano Battelli, Michal Feckan
doaj +2 more sources
Journal of Difference Equations and Applications, 2021 We consider non-autonomous N-periodic discrete dynamical systems of the form (Formula presented.) having when (Formula presented.) an open continuum of initial conditions such that the corresponding sequences are N-periodic. From the study of some variational equations of low order, we obtain successive maps, that we call discrete Melnikov functions ...
Gasull, Armengol, Valls, Clàudia
openaire +3 more sources
Second Order Melnikov Functions of Piecewise Hamiltonian Systems [PDF]
International Journal of Bifurcation and Chaos, 2020 In this paper, we consider the general perturbations of piecewise Hamiltonian systems. A formula for the second order Melnikov functions is derived when the first order Melnikov functions vanish. As an application, we can improve an upper bound of the number of bifurcated limit cycles of a piecewise Hamiltonian system with quadratic polynomial ...
Françoise, Jean-Pierre +2 more
openaire +1 more source
Confusion threshold study of the Duffing oscillator with a nonlinear fractional damping term
Journal of Low Frequency Noise, Vibration and Active Control, 2021 In this study, the critical conditions for generating chaos in a Duffing oscillator with nonlinear damping and fractional derivative are investigated. The Melnikov function of the Duffing oscillator is established based on Melnikov theory.
Wang Mei-Qi +5 more
doaj +1 more source
Brodogradnja, 2021 The trimaran vessel rolls strongly at low forward speed and may capsize in high sea conditions due to chaos and loss of stability, which is not usually considered in conventional limit-based criteria.
Yihan Zhang +3 more
doaj +1 more source
Infinite orbit depth and length of Melnikov functions [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2019 In this paper we study polynomial Hamiltonian systems dF = 0 in the plane and their small perturbations: dF + \epsilon \omega = 0 . The first nonzero Melnikov function M_{\mu } = M_{\mu }(F,\gamma ,\omega )
Mardešić, Pavao +3 more
openaire +4 more sources