Results 21 to 30 of about 27,933 (207)
On the expansion of the Melnikov function near a double heteroclinic loop with two nilpotent cusps
上海师范大学学报. 自然科学版, 2020 In this paper, we give all the different topological types of phase portrait for the unperturbed Liénard system ẋ=y, ẏ=-g(x) in the case that deg g(x)=7 and the system has 2, 3, 4 and 5 singular points, respectively.
MIAO Jiale, YANG Junmin
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Existence of Solitary Waves in a Perturbed KdV-mKdV Equation
Journal of Mathematics, 2021 In this paper, we establish the existence of a solitary wave in a KdV-mKdV equation with dissipative perturbation by applying the geometric singular perturbation technique and Melnikov function.
Chengqun Li, Minzhi Wei, Yuanhua Lin
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Limit Cycle Bifurcations from Centers of Symmetric Hamiltonian Systems Perturbing by Cubic Polynomials [PDF]
, 2012 In this paper, we consider some cubic near-Hamiltonian systems obtained from perturbing the symmetric cubic Hamiltonian system with two symmetric singular points by cubic polynomials.
Gao, Bin +2 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2017 In this article we study the existence and positions of limit cycles in piecewise smooth perturbations of planar Hamiltonian centers. By using the regularization method we provide an analytical expression for the first order Melnikov function frequently ...
Luis Mello +2 more
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Applied Sciences, 2023 The dynamic vibration absorber (DVA) is widely used in engineering models with complex vibration modes. The research on the stability and periodic motions of the DVA model plays an important role in revealing its complex vibration modes and energy ...
Ziyu Guo +3 more
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Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics [PDF]
, 2019 We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their ...
Krajňák, Vladimír, Wiggins, Stephen
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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′=ε F(t,x,ε ). By one hand, the classical (stroboscopic) averaging method provides asymptotic estimates for its solutions in terms of some uniquely
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Morse and Melnikov functions for NLS Pde's [PDF]
Communications in Mathematical Physics, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Y., McLaughlin, David W.
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Limit cycle bifurcations in a planar piecewise quadratic system with multiple parameters
Advances in Difference Equations, 2020 This paper is concerned with the number of limit cycles bifurcating from a period annulus for some planar piecewise smooth non-Hamiltonian systems. We construct a planar piecewise quadratic system with multiple parameters, obtain its lower bound for the ...
Shuhua Gong, Maoan Han
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On the Number of Limit Cycles of a Piecewise Quadratic Near-Hamiltonian System
Abstract and Applied Analysis, 2014 This paper is concerned with the problem for the maximal number of limit cycles for a quadratic piecewise near-Hamiltonian system. By using the method of the first order Melnikov function, we find that it can have 8 limit cycles.
Jing Tian
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