Results 171 to 180 of about 27,933 (207)

Perturbed normalizers and Melnikov functions

Journal of Mathematical Analysis and Applications, 2018
Consider a \(C^{\infty}\) smooth family of real planar vector fields \(\left(X_\varepsilon\right)_\varepsilon\) of the form \[ X_\varepsilon (x) \, = \, X_0(x) + \varepsilon X_1(x) + \varepsilon^2 X_2(x) + \, \ldots \, + \varepsilon^n X_n(x) + \mathcal{O}\left(\varepsilon^{n+1}\right), \] for some integer \(n \geq 1\), \(x \in \mathbb{R}^2\) and ...
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The Evans Function and Generalized Melnikov Integrals

SIAM Journal on Mathematical Analysis, 1999
Summary: The Evans function, \(E(\lambda)\), is an analytic function whose zeros coincide with the eigenvalues of the operator \(L\), obtained by linearizing about a travelling wave. The algebraic multiplicity of the eigenvalue \(\lambda_0\) is equal to the order of the zero of \(E(\lambda)\).
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MELNIKOV FUNCTIONS AND PERTURBATION OF A PLANAR HAMILTONIAN SYSTEM

Chinese Annals of Mathematics, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiang, Qibao, Han, Mao'an
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Melnikov functions and Bautin ideal

Qualitative Theory of Dynamical Systems, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Melnikov function and homoclinic chaos induced by weak perturbations

Physical Review E, 1993
The effect of noise on the possible occurrence of chaos in systems with a homoclinic orbit (e.g., the Duding equation) was recently considered by Bulsara, Schieve, and Jacobs [Phys. Rev. A 41, 668 (1990)], and Schieve and Bulsara [Phys. Rev. A 41, 1172 (1990)], who adopted an approach based on a redefinition of the Melnikov function.
, Simiu, , Frey
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A note on higher order Melnikov functions

Qualitative Theory of Dynamical Systems, 2005
The paper comments some facts related to the weakened 16th Hilbert's problem about limit cycles. The authors deal with small polynomial perturbations of Hamiltonian systems in the plane \(dH-\varepsilon \omega=0\) such that the first displacement map near a periodic orbit of the unperturbed system is of the form \(\Delta H=\varepsilon^kM_k(h)+O ...
Jebrane, Ahmed, Żołądek, Henryk
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Finding More Limit Cycles Using Melnikov Functions

2012
In Chap. 9, an idea for finding more limit cycles is introduced, which combines the bifurcation of limit cycles from centers, homoclinic and heteroclinic loops. A generalized theorem is presented. In particular, two polynomial systems are studied. By using the theorems and results obtained in Chaps.
Maoan Han, Pei Yu
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Melnikov functions in the rigid body dynamics

2019
we review our recent results about perturbations of two cases in the rigid body dynamics: the hess–appelrot case and the lagrange case.
Paweł Lubowiecki, Henryk Żołądek
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Fundamental Theory of the Melnikov Function Method

2012
Chapter 6 introduces the fundamental theory of Melnikov function method. Basic definitions and fundamental lemmas are presented. A main theory on the number of limit cycles is given.
Maoan Han, Pei Yu
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Applications of the signs of Melnikov's function

Applied Mathematics and Mechanics, 1992
The Melnikov function technique is applied to study the existence and stability of periodic solutions of a planar autonomous system under a small perturbation.
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