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Separatrices and limit cycles of strongly nonlinear oscillators by the perturbation-incremental method

✍ Scribed by Z. Xu; H. S. Y. Chan; K. W. Chung

Publisher
Springer Netherlands
Year
1996
Tongue
English
Weight
841 KB
Volume
11
Category
Article
ISSN
0924-090X

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✦ Synopsis

The perturbation-incremental method is applied to determine the separatrices and limit cycles of strongly nonlinear oscillators. Conditions are derived under which a limit cycle is created or destroyed. The latter case may give rise to a homoclinic orbit or a pair of heteroclinic orbits. The limit cycles and the separatrices can be calculated to any desired degree of accuracy. Stability and bifurcations of limit cycles will also be discussed.

πŸ“œ SIMILAR VOLUMES

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The semi-stable limit cycle and bifurcation of strongly non-linear oscillators of the form xK #g(x)" f (x, xR , )xR is studied by the perturbation-incremental method. Firstly, the ordinary di!erential equation is transformed into an integral equation by a non-linear time transformation, then the ini

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The elliptic perturbation method is applied to the study of the periodic solutions of strongly quadratic non-linear oscillators of the form x¨+ c1 x + c2 x 2 = ef(x, x˙), in which the Jacobian elliptic functions are employed. The generalized Van der Pol equation with f(x, x˙) = m0 + m1 x -m2 x 2 is