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Digitale Medien

Homoclinic Connections in Strongly Self-Excited Nonlinear Oscillators: The Melnikov Function and the Elliptic Lindstedt–Poincaré Method (2000)

Belhaq, Mohamed ; Fiedler, Bernold ; Lakrad, Faouzi

Springer

Nonlinear dynamics 23 (2000), S. 67-86

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ISSN: 1573-269X

Schlagwort(e): homoclinic bifurcations criteria ; elliptic Lindstedt–Poincaré method ; Melnikov function

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract A criterion to predict bifurcation of homoclinic orbits instrongly nonlinear self-excited one-degree-of-freedom oscillator $$\ddot x + c_1 x + c_2 f(x) = \varepsilon g(\mu ,x,\dot x),$$ is presented. TheLindstedt–Poincaré perturbation method is combined formally withthe Jacobian elliptic functions to determine an approximation of thelimit cycles near homoclinicity. We then apply a criterion forpredicting homoclinic orbits, based on the collision of the bifurcatinglimit cycle with the saddle equilibrium. In particular we show that thiscriterion leads to the same results, formally and to leading order, asthe standard Melnikov technique. Explicit applications of this criterionto quadratic or cubic nonlinearities f(x) are included.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1023/A:1008316010341

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