Results 171 to 180 of about 26,339 (212)

A PHYSICAL INTERPRETATION OF MELNIKOV’S METHOD

International Journal of Bifurcation and Chaos, 1992
This paper is concerned with analyzing Melnikov’s method in terms of the flow generated by a vector field in contrast to the approach based on the Poincare map and giving a physical interpretation of the method. It is shown that the direct implication of a transverse crossing between the stable and unstable manifolds to a saddle point of the Poincare ...
openaire   +1 more source

EXPONENTIAL DICHOTOMIES, HOMOCLINIC ORBITS AND METHODS OF MELNIKOV

Acta Mathematica Scientia, 1996
The main goal of this paper is to investigate the existence of transversal homoclinic orbits of the perturbed equation \[ dx/dt= g(x)+ \varepsilon h(t,x,\varepsilon).\tag{\(*\)} \] The authors construct a Melnikov-type function which yields transversal homoclinic orbits also when the perturbation does not depend on \(t\).
Zeng, Weiyao, Qian, Xiangzheng, Wang, Zhicheng   +2 more
openaire   +2 more sources

Melnikov's method and averaging

Celestial Mechanics, 1982
Consider the differential equation \(\dot x=f^ 0(x)+\epsilon f^ 1(\omega t,x;\epsilon)\), \(x\in D\subset R^ n\) where \(f^ 0\) and \(f^ 1\) are sufficiently smooth, \(f^ 1\) is \(2\pi\)-periodic in \(\omega\) t and \(\epsilon\) is a small positive parameter. Let the unperturbed system \(\dot x=f^ 0(x)\) have a hyperbolic point.
openaire   +2 more sources

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
openaire   +1 more source

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.
openaire   +1 more source

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
openaire   +2 more sources

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 ...
openaire   +1 more source

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
openaire   +1 more source

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 ...
openaire   +1 more source

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.
openaire   +1 more source