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Strong Resonances at Hopf Bifurcations in Control Systems

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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.

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Authors and Affiliations

  1. National Research Institute for Information and Automation (INRIA), Rocquencourt, France

    P.-A. Bliman

  2. Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    A. M. Krasnosel'skii & D. I. Rachinskii

Authors
  1. P.-A. Bliman
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  2. A. M. Krasnosel'skii
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  3. D. I. Rachinskii
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Bliman, PA., Krasnosel'skii, A.M. & Rachinskii, D.I. Strong Resonances at Hopf Bifurcations in Control Systems. Automation and Remote Control 62, 1783–1802 (2001). https://doi.org/10.1023/A:1012786122737

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