Results 181 to 190 of about 5,152,512 (204)

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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Expansion Coefficients and Their Relation for Melnikov Functions Near Polycycles

Journal of Differential Equations
Assuming a particular condition, the authors present novel results concerning expansion coefficients and their interrelation within the first-order Melnikov functions. These results, derived for m-polycycles (where m is a positive integer) with hyperbolic saddles, lead to a comprehensive bifurcation theory for predicting limit cycles near these ...
Feng Liang, Maoan Han
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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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Exponential dichotomies and Melnikov functions for singularly perturbed systems

Nonlinear Analysis: Theory, Methods & Applications, 1999
Consider the singularly perturbed differential system \[ dx/dt = f(x,y)+ \varepsilon h_1 (t,x,y,\varepsilon),\quad \varepsilon dy/dt = g (x,y) + \varepsilon h_2 (t,x,y,\varepsilon),\tag \(*\) \] with \(x \in \mathbb{R}^n\), \(y\in \mathbb{R}^m\) and where \(\varepsilon \geq 0\) is a small parameter, \(f,g, h_1\) and \(h_2\) are \(C^2\)-smooth, and ...
Weiyao, Zeng, Jiaowan, Luo
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Melnikov Functions in Quadratic Perturbations of Generalized Lotka–Volterra Systems

Journal of Dynamical and Control Systems, 2015
The author presents a detailed analysis of Melnikov functions which arise in quadratic perturbations of generalized Lotka-Volterra vector fields with the first integral \(x^{\alpha}y^{\beta}(1-x-y)\) and, in particular, proves that the maximal number of limit cycles in the generic case is equal to 2 and in the Hamiltonian triangle case is equal to 3.
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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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