Results 121 to 130 of about 774 (145)

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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ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS

International Journal of Bifurcation and Chaos, 2012
In the study of the perturbation of Hamiltonian systems, the first order Melnikov functions play an important role. By finding its zeros, we can find limit cycles. By analyzing its analytical property, we can find its zeros. The main purpose of this article is to summarize some methods to find its zeros near a Hamiltonian value corresponding to an ...
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Second order Melnikov function and its application

Physics Letters A, 1990
Abstract Based on Melnikov's method, the second order Melnikov function for the study of subharmonic and ultrasubharmonic orbits in a class of planar Hamiltonian systems is derived. Using this function the existence criterion of subharmonic and ultrasubharmonic orbits is set. A nonlinear oscillator subject to perturbation as example is discussed.
Zengrong Liu, Guoqing Gu
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Wavelet and Melnikov function analysis of oscillations of a submarine

The Journal of the Acoustical Society of America, 1996
The explicit time description, computer modeling, and Melnikov function approach for the problem of detecting signals from oscillations of submarines are given. This problem in the Galerkin approximation is reduced to the problem of solving the system of differential equations with polynomial nonlinearities and variable coefficients.
Michael G. Zeitlin, Antonina N. Fedorova
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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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Reply to ‘‘Melnikov function and homoclinic chaos induced by weak perturbations’’

Physical Review E, 1993
For the case of weak perturbations, our theory is shown to reproduce exactly the results of Simiu and Frey [Phys. Rev. E 48, 3185 (1993)]. In the presence of weak noise, the two approaches yield different results. This can be traced to the neglect of diffusion effects in the Simiu-Frey theory; the inclusion of these effects, via an ensemble-averaged ...
, Bulsara, , Schieve, , Jacobs
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A FAST-MANIFOLD APPROACH TO MELNIKOV FUNCTIONS FOR SLOWLY VARYING OSCILLATORS

International Journal of Bifurcation and Chaos, 1996
A new approach to obtaining the Melnikov function for homoclinic orbits in slowly varying oscillators is proposed. The present method applies the usual two-dimensional Melnikov analysis to the “fast” dynamics of the system which lie on an invariant manifold. It is shown that the resultant Melnikov function is the same as that obtained in the usual way
Chen, Shyh-Leh, Shaw, Steven W.
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Melnikov vector function for high-dimensional maps

Physics Letters A, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Evans' Function, Melnikov's Integral, and Solitary Wave Instabilities

1993
Publisher Summary This chapter describes the Evans' function, Melnikov's integral and solitary wave instabilities. The chapter mentions recent results on (1) the method for detecting the eigenvalues of systems of ordinary differential equations with asymptotically constant coefficients, (2) applications of this method to the detection of ...
Robert L. Pego, Michael I. Weinstein
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