Results 91 to 100 of about 308 (136)

Equivalence of the Melnikov Function Method and the Averaging Method

Qualitative Theory of Dynamical Systems, 2015
In this paper, the authors study the problem of equivalence between the Melnikov method and the averaging method for studying the number of limit cycles which can bifurcate from the period annulus of planar analytic differential systems.
Maoan Han, Valery G. Romanovski, Xiang Zhang   +2 more
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Melnikov’s method for a general nonlinear vibro-impact oscillator

Nonlinear Analysis: Theory, Methods & Applications, 2009
The classical Melnikov's method is applied to a second order differential equation with impact effects. The equation is a perturbation of a Hamiltonian system with a homoclinic orbit to the origin. Then the first-order Melnikov function can be obtained analytically in the usual way. The method is applied to a double-well Duffing oscillator with impacts,
Xu, Wei, Feng, Jinqian, Rong, Haiwu
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Melnikov method for discontinuous planar systems

Nonlinear Analysis: Theory, Methods & Applications, 2007
This paper deals with the existence of a homoclinic solution in planar systems with discontinuous right-hand side. In fact, these type of systems are more used in practical problems than the classical planar differential systems and this article serves to a generalization of the Melnikov function to these discontinuous right-hand side systems.
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CHAOTIC ATTITUDE MOTION OF GYROSTAT SATELLITE VIA MELNIKOV METHOD

International Journal of Bifurcation and Chaos, 2001
In this paper Deprit's variables are used to describe the Hamiltonian equations for attitude motions of a gyrostat satellite spinning about arbitrarily body-fixed axes. The Hamiltonian equations for the attitude motions of the gyrostat satellite in terms of the Deprit's variables and under small viscous damping and nonautonomous perturbations are ...
Kuang, Jinlu, Tan, Soonhie, Arichandran, Kandian, Leung, A. Y. T.   +3 more
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Melnikov's method with applications

2009
This thesis gives a detailed discussion of Melnikov's method, which is an analytical tool to study global bifurcations that occur in homoclinic or heteroclinic loops, or in one-parameter families of periodic orbits of a perturbed system. Basic results of the Melnikov theory relating the number, positions and multiplicities of the limit cycles by the ...
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A Melnikov Method for Strongly Odd Nonlinear Oscillators

Japanese Journal of Applied Physics, 1998
In this paper, explicit calculations that extend the applicability of the Melnikov method to include strongly odd nonlinear and large forcing amplitude oscillating systems, are presented. We consider the response of the strongly nonlinear oscillating system governed by an equation of motion containing a parameter ε which need not be small ...
Zheng-Ming Ge, Fu-Neng Ku
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Melnikov’s method applied to accidental phase modulation phenomenon

The European Physical Journal Special Topics, 2021
The performance of clock recovery phase-locked loop (PLL) can be severely degraded by unwanted spurious phase modulation, due to noise and nonlinearities associated with the transmission medium. Consequently, choosing appropriate circuit parameters to avoid or at least reduce these undesirable effects plays a crucial role in achieving a successful PLL ...
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Melnikov's method applied to the double pendulum

Zeitschrift f�r Physik B Condensed Matter, 1994
Melnikov's method is applied to the planar double pendulum proving it to be a chaotic system. The parameter space of the double pendulum is discussed, and the integrable cases are identified. In the neighborhood of the integrable case of two uncoupled pendulums Melnikov's integral is evaluated using residue calculus.
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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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