Results 101 to 110 of about 44,286,818 (153)
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.
Xiaobiao Lin
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Melnikov's method and averaging
Celestial Mechanics, 1982Consider 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.
J. Sanders
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A PHYSICAL INTERPRETATION OF MELNIKOV’S METHOD
International Journal of Bifurcation and Chaos, 1992This 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 ...
Yohannes Ketema
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A numerical implementation of Melnikov's method
Physics Letters A, 1987Abstract A numerical implementation of Melnikov's method is proposed. The procedure is based on the convergence of the integral and the uniqueness of the boundary of the horseshoe region in the parameter space under certain conditions. Several examples are calculated.
F.H. Ling, G.W. Bao
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Melnikov's method applied to the double pendulum
Zeitschrift f�r Physik B Condensed Matter, 1994Melnikov'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.
H. Dullin
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Melnikov’s method for a general nonlinear vibro-impact oscillator
Nonlinear Analysis: Theory, Methods & Applications, 2009The 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's method with applications
2009This 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 ...
Yan-Kin Chow
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A numerical study of the applicability of Melnikov's method
Physics Letters A, 1987Abstract Melnikov's method can be used to predict the appearance of the homoclinic and also the heteroclinic tangency. The applicability of the method is studied by using numerically calculated invariant manifolds of the Poincare map of a soft spring oscillator.
F.-H. Ling
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