Results 11 to 20 of about 22,008 (172)
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
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Electronic Journal of Qualitative Theory of Differential EquationsThis addendum presents a relevant stronger consequence of the main theorem of the paper “Higher order stroboscopic averaged functions: a general relationship with Melnikov functions”, Electron. J. Qual. Theory Differ. Equ. 2021, No. 77.
Douglas Novaes
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An Algorithm for Melnikov Functions and Application to a Chaotic Rotor [PDF]
SIAM Journal on 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.
Jian-Xin, X., Yan, R., Zhang, W.
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Using Melnikov functions of any order for studying limit cycles
Journal of Mathematical Analysis and Applications, 2017 The planar system investigated in the paper is related to Hilbert's 16th problem. The author studies a class of quadratic Hamiltonian systems perturbed with general quadratic polynomials in order to identify the maximum number of limit cycles. He derived the Melnikov functions arisen from the displacement function of the first return map.
Gheorghe Tigan
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A generalization of Françoise's algorithm for calculating higher order Melnikov functions
Bulletin des Sciences Mathématiques, 2002 In [J. Differential Equations 146 (2) (1998) 320–335], Françoise gives an algorithm for calculating the first nonvanishing Melnikov function Mℓ of a small polynomial perturbation of a Hamiltonian vector field and shows that Mℓ is given by an Abelian integral.
Jebrane, Ahmed +2 more
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BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION
Journal of Applied Analysis & Computation, 2015 Summary: In this short paper, we present some remarks on the role of the rstorder Melnikov functions in studying the number of limit cycles of piecewisesmooth near-Hamiltonian systems on the plane.
Han, Maoan, Sheng, Lijuan
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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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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
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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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