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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
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Some remarks on the Melnikov function [PDF]
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
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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
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Experimental measurement of the Melnikov function [PDF]
Physics of Fluids, 2015 We 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 both stratified with a linear density gradient using salted water and viscous in order to prevent Ekman pumping and ...
Meunier, Patrice +3 more
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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
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An Algorithm for Melnikov Functions and Application to a Chaotic Rotor [PDF]
SIAM Journal of Scientific Computing, 2005 The paper deals with a problem often encountered in practice: how to use Melnikov's method to analyze chaotic behavior of a nonlinear system whose homoclinic (or heteroclinic) orbits cannot be obtained analytically. First, the model for a rigid shaft of rotor on a low-speed balance platform is derived.
Weinian Zhang
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Higher order Melnikov function for a quartic hamiltonian with cuspidal loop
Discrete and Continuous Dynamical Systems, 2002 The authors consider the polynomial perturbations \[ X_{\varepsilon}=X_H+ \varepsilon f(x,y,\varepsilon)\frac{\partial}{\partial x}+ \varepsilon g(x,y,\varepsilon)\frac{\partial}{\partial y}, \] where \(f(x,y,\varepsilon)\) and \(g(x,y,\varepsilon)\) are polynomials in \(x,y\) with coefficients depending analytically on the small parameter ...
Yulin Zhao
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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
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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
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