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Degenerate Hopf Bifurcations in Discontinuous Planar Systems

✍ Scribed by B. Coll; A. Gasull; R. Prohens

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
150 KB
Volume
253
Category
Article
ISSN
0022-247X

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✦ Synopsis

We study the stability of a singular point for planar discontinuous differential equations with a line of discontinuities. This is done, for the most generic cases, by computing some kind of Lyapunov constants. Our computations are based on the Ε½ . so called R, , p, q -generalized polar coordinates, introduced by Lyapunov, and they are essentially different from the ones used in the smooth case. These Lyapunov constants are also used to generate limit cycles for some concrete examples.

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## Abstract A stability criterion for nonlinear oscillations in power systems is proposed. It consists of calculation of a limit cycle by application of Hopf bifurcation theory and nonlinear transformation of the coordinates using invariant manifolds. The proposed method is verified in a single‐mac