Results 181 to 190 of about 26,339 (212)

A practical use of the Melnikov homoclinic method

Journal of Mathematical Physics, 2009
Using cutoff functions and periodic extensions, we prove that the Melnikov homoclinic method gives a criterium to show that for a finite time interval [−T,T], with T arbitrarily large, the perturbed system is conjugated to a chaotic one for quite general classes of perturbation functions.
Castilho, César, Marchesin, Marcelo
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Using Melnikov's method to solve Silnikov's problems

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1990
SynopsisA function space approach is employed to obtain bifurcation functions for which the zeros correspond to the occurrence of periodic or aperiodic solutions near heteroclinic or homoclinic cycles. The bifurcation function for the existence of homoclinic solutions is the limiting case where the period is infinite.
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Melnikov's method for rigid bodies subject to small perturbation torques

Archive of Applied Mechanics, 1996
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Tong, X., Tabarrok, B.
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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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The Multiple Scales Method, Homoclinic Bifurcation and Melnikov's Method for Autonomous Systems

International Journal of Bifurcation and Chaos, 1998
Melnikov's method is a well-established technique for detecting homoclinic bifurcation of perturbed autonomous or forced systems. This method uses a regular perturbation expansion in terms of a small parameter in the system. Whilst the approach correctly estimates the parameter values for the bifurcation and transverse intersections of separatrices ...
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Markov and Melnikov based methods for vessel capsizing criteria

Ocean Engineering, 2013
Abstract Vessel capsizing analysis in random beam sea has been approached using different analytical methods in the past decades. However, due to the strong softening nonlinear stiffness and stochastic excitation, there is still no general method of dealing with capsizing prediction in a random sea.
Zhiyong Su, Jeffrey M. Falzarano
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On the Equivalence of the Melnikov Functions Method and the Averaging Method

Qualitative Theory of Dynamical Systems, 2016
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On some applications of Melnikov's method to chaos and subharmonics

Bulletin of the Australian Mathematical Society, 1996
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Melnikov method and exponentially small splitting of separatrices

Physica D: Nonlinear Phenomena, 1997
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Melnikov method and elliptic equations with critical exponent

1994
We consider the existence of ground states for the problem Delta u + K(\x\)U-(n+2/(n-2)) = 0 where K(\x\) is a positive, bounded, continuous function. We use dynamical systems methods, especially the method of the Melnikov function to find conditions under which this problem admits a ground state or a singular ground state.
JOHNSON, RUSSELL ALLAN, X. B. Pan, Y. F. Yi   +2 more
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