Results 31 to 40 of about 27,933 (207)

Exploring Limit Cycle Bifurcations in the Presence of a Generalized Heteroclinic Loop

Mathematics, 2023
This work revisits the number of limit cycles (LCs) in a piecewise smooth system of Hamiltonian with a heteroclinic loop generalization, subjected to perturbed functions through polynomials of degree m.
Erli Zhang, Stanford Shateyi
doaj   +1 more source

Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

, 2002
We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface.
Abraham R, Arnold V I, Baldomà M, Cartwright J H E, Delshams A, Delshams A, Easton R W, Easton R W, Feingold M, H E Lomel, Holmes P, J D Meiss, LomelíH E, LomelíH E, MacKay R S, MacKay R S, MacKay R S, Meiss J D, Mezic I, Piro O, Rom-Kedar V, Suris Y B, Treshev D V, Wiggins S   +23 more
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Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold

, 2018
We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family.
Bastos, Jéfferson L. R., Buzzi, Claudio A., Llibre, Jaume, Novaes, Douglas D.   +3 more
core   +1 more source

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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Analysis of Tangential Nonlinear Vibration on Machine Hydrostatic Slide

Shock and Vibration, 2019
In this paper, the nonlinear dynamic responses of the hydrostatic slide were investigated and the effects of damping and external force to control the vibration system were discussed.
Zhongkui Zhang, Feng Gao, Yan Li, Han Zhang   +3 more
doaj   +1 more source

Resonant motions in the presence of degeneracies for quasi-periodically perturbed systems

, 2012
We consider one-dimensional systems in the presence of a quasi-periodic perturbation, in the analytical setting, and study the problem of existence of quasi-periodic solutions which are resonant with the frequency vector of the perturbation.
Andronov, Arnold, Bryuno, Bryuno, Delshams, Guckenheimer, GUIDO GENTILE, LIVIA CORSI, Meyer, Nayfeh, Xu   +10 more
core   +3 more sources

Exponential dichotomies, heteroclinic orbits, and Melnikov functions

Journal of Differential Equations, 1990
The authors consider an n-dimensional perturbed system (*) \(dz/dt=g(z)+h(t,z,\epsilon),\) where the perturbation term h(t,z,\(\epsilon\)) is bounded, \(\epsilon\) being a multidimensional parameter, and they give, using the method of Lyapunov-Schmidt, a sufficient condition for the existence of a bounded solution of (*) as the solvability condition of
Battelli, Flaviano, Lazzari, Claudio
openaire   +1 more source

Periodic Solutions and Stability Analysis for Two-Coupled-Oscillator Structure in Optics of Chiral Molecules

Mathematics, 2022
Chirality is an indispensable geometric property in the world that has become invariably interlocked with life. The main goal of this paper is to study the nonlinear dynamic behavior and periodic vibration characteristic of a two-coupled-oscillator model
Jing Li, Yuying Chen, Shaotao Zhu
doaj   +1 more source

Nilpotence of orbits under monodromy and the length of Melnikov functions

Physica D: Nonlinear Phenomena, 2021
Let $F\in\mathbb{C}[x,y]$ be a polynomial, $\gamma(z)\in \pi_1(F^{-1}(z))$ a non-trivial cycle in a generic fiber of $F$ and let $\omega$ be a polynomial $1$-form, thus defining a polynomial deformation $dF+\epsilon\omega=0$ of the integrable foliation given by $F$.
Mardešić, Pavao, Novikov, Dmitry, Ortiz-Bobadilla, Laura, Pontigo-Herrera, Jessie   +3 more
openaire   +4 more sources

One More Thing on the Subject: Prediction of Chaos in a Josephson Junction with Quadratic Damping by the Melnikov Technique, Possible Probabilistic Control over Oscillations

Applied Sciences
Many authors analyze the prediction of chaos in a Josephson junction with quadratic damping by the Melnikov technique. Due to the lack of an explicit presentation of the Melnikov integral, the researchers apply numerical methods and illustrative examples
Nikolay Kyurkchiev, Tsvetelin Zaevski, Anton Iliev, Vesselin Kyurkchiev, Asen Rahnev   +4 more
doaj   +1 more source