Results 11 to 20 of about 26,339 (212)

Melnikov's Method and Codimension-Two Bifurcations in Forced Oscillations

Journal of Differential Equations, 2002
The author considers a periodic perturbation of a planar Hamiltonian system of the form \[ \dot{x}=JD_x H(x)+\epsilon g(x,\omega t;\mu),\qquad x\in \mathbb{R}^2. \] It is assumed that the unperturbed system has a one-parameter family of periodic orbits \(q^{\alpha}(t)\) analytic with respect to \(\alpha\).
Kazuyuki Yagasaki
openaire   +3 more sources

Canonical Melnikov theory for diffeomorphisms [PDF]

, 2007
We study perturbations of diffeomorphisms that have a saddle connection between a pair of normally hyperbolic invariant manifolds. We develop a first-order deformation calculus for invariant manifolds and show that a generalized Melnikov function or ...
Abraham R, Baldomà M, Bolotin S, Cresson J Wiggins S, de la Llave R, Delshams A, Delshams A, Easton R W, Gómez A, Hirsch M W, Hirsch M W, Héctor E Lomelí, James D Meiss, Lomeli H E, Lomeli H E, Lomeli H E Ramírez-Ros R, McMillan E M, Melnikov V K, Poincaré H, Rafael Ramírez-Ros, Thom R Levine H Wall C T   +20 more
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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
doaj   +1 more source

A short proof of chaos in an atmospheric system [PDF]

, 2002
We will prove the presence of chaotic motion in the Lorenz five-component atmospheric system model using the Melnikov function method developed by Holmes and Marsden for Hamiltonian systems on Lie Groups.Comment: PACS: 02.20.Sv; 02.30.Hg; 02.40.-k; 92.60.
Bokhove, Bokhove, Camassa, Holmes, Lorenz, Melnikov, Mircea Puta, Petre Birtea, Răzvan Tudoran, Tudor S. Ratiu, Wiggins   +10 more
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A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations

Journal of Mathematics, 2021
This work extends the high-order Melnikov method established by FJ Chen and QD Wang to heteroclinic orbits, and it is used to prove, under a certain class of perturbations, the heteroclinic orbit in a planar vector field that remains unbroken ...
Yi Zhong
doaj   +1 more source

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, Hu, Zhaoping, Romanovski, Valery G.   +2 more
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Homoclinic crossing in open systems: Chaos in periodically perturbed monopole plus quadrupolelike potentials [PDF]

, 2002
The Melnikov method is applied to periodically perturbed open systems modeled by an inverse--square--law attraction center plus a quadrupolelike term. A compactification approach that regularizes periodic orbits at infinity is introduced.
A. E. Motter, A. Kenfack, A.M. Ozorio de Almeida, C. Chicone, D. Hennig, E. Ott, F.Kh. Abdullaev, G.D. Birkhoff, H. Bai-lin, H. Dankowicz, H. Poincaré, I.S. Gradshteyn, I.W. Stewart, J. Casasayas, J. Guckenheimer, J. Koiller, J. Moser, O.E. Gerhard, O.E. Gerhard, P. S. Letelier, P.S. Letelier, P.S. Letelier, R. McGehee, R. Moeckel, S. Chandrasekhar, S. Smale, T. Ahn, V.I. Arnold, V.K.Melnikov, X. Yao, Z. Xia   +30 more
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Poincaré-Melnikov-Arnold Method for Twist Maps [PDF]

, 1999
The Poincar\'e--Melnikov--Arnold method is the standard tool for detecting splitting of invariant manifolds for systems of ordinary differential equations close to ``integrable'' ones with associated separatrices. This method gives rise to an integral (continuous sum) known as the Melnikov function (or Melnikov integral).
Delshams Valdés, Amadeu, Ramírez Ros, Rafael   +1 more
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NONLINEAR ROLLING STABILITY AND CHAOS RESEARCH OF TRIMARAN VESSEL WITH VARIABLE LAY-OUTS IN REGULAR AND IRREGULAR WAVES UNDER WIND LOAD

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, Ping Wang, Yachong Liu, Jingfeng Hu   +3 more
doaj   +1 more source

The Onset of Chaos in Spinning Particle Models [PDF]

, 2003
The onset of chaos in one-dimensional spinning particle models derived from pseudoclassical mechanical hamiltonians with a bosonic Duffing potential is examined.
Berezin, Bombelli, Casalbuoni, Cornish, H.T. Cho, Heumann, Holmes, J.-K. Kao, Levin, Melnikov, Rietdijk, Rietdijk, Suzuki   +12 more
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