Strong Resonances at Hopf Bifurcations in Control Systems

  • Authors:

  • P.-A. Bliman;A. M. Krasnosel'skii;D. I. Rachinskii

  • Affiliations:

  • National Research Institute for Information and Automation (INRIA), Rocquencourt, France;Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia;Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

  • Venue:
  • Automation and Remote Control
  • Year:
  • 2001

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Abstract

The 0:1 and 1:1 resonances at Hopf bifurcations in control systems with a parameter are investigated. Conditions for the generation of cycles in the neighborhood of the equilibrium position and at infinity are formulated. Nonlinearities with a principle quadratic part and with a principle homogeneous part of the general (nonpolynomial) type in the neighborhood of the equilibrium position are separately studied. The main case of bounded saturation nonlinearities at infinity is also studied.