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Strong Resonances at Hopf Bifurcations in Control Systems

โœ Scribed by P.-A. Bliman; A.M. Krasnosel'skii; D.I. Rachinskii

Book ID
110316629
Publisher
SP MAIK Nauka/Interperiodica
Year
2001
Tongue
English
Weight
257 KB
Volume
62
Category
Article
ISSN
0005-1179

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๐Ÿ“œ SIMILAR VOLUMES

Hopf bifurcations in resonance 2:1
Hopf bifurcations in resonance 2:1
โœ A.M. Krasnosel'skii; D.I. Rachinskii; K. Schneider ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 182 KB

In this paper Hopf bifurcations for equations of control theory are studied in strong resonance case 2:1. The harmonic linearization approach and topological methods allow to give the sharp analysis of the problem for the case of quadratic principal nonlinearity.

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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 ลฝ . so called R, , p, q -generalized polar coordinates,