Results 1 to 10 of about 774 (145)
Third Order Melnikov Functions of a Cubic Center under Cubic Perturbations
Mathematics, 2022 In this paper, cubic perturbations of the integral system (1+x)2dH where H=(x2+y2)/2 are considered. Some useful formulae are deduced that can be used to compute the first three Melnikov functions associated with the perturbed system.
Yanwei Liu, Tonghua Zhang, Xia Liu
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Higher order stroboscopic averaged functions: a general relationship with Melnikov functions
Electronic Journal of Qualitative Theory of Differential Equations, 2021 In the research literature, one can find distinct notions for higher order averaged functions of regularly perturbed non-autonomous $T$-periodic differential equations of the kind $x'=\varepsilon F(t,x,\varepsilon)$.
Douglas Novaes
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Nonlinear behavior and energy harvesting performance of a new tunable quasi-zero stiffness system [PDF]
Scientific ReportsEnergy harvesting from vibrations is a popular research topic. However, it is difficult to change the values of its dynamic stiffness characteristics during the operation of device.
Xinzong Wang, Xiaofang Kang, Ao Zhang
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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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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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Athens Journal of Architecture, 2023 The research focuses on the application of the elements of the theory of linear urbanism to the current solution for the rural settlements, from which life is lost and they are becoming open-air museums.
Nikoleta Slováková
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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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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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Mathematics, 2023 Systems composed of piecewise smooth differential (PSD) mappings have quantitatively been searched for answers to a substantial issue of limit cycle (LC) bifurcations. In this paper, LC numbers (LCNs) of a PSD system (PSDS) consisting of four regions are
Erli Zhang, Jihua Yang, Stanford Shateyi
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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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