WIAS Preprint No. 921, (2004)

Hopf bifurcations and simple structures of periodic solution sets in systems with the Preisach nonlinearity



Authors

  • Brokate, Martin
    ORCID: 0000-0003-4660-9180
  • Rachinskii, Dmitri

2010 Mathematics Subject Classification

  • 34C55 34D20 34D10

Keywords

  • Hysteresis, forced periodic oscillations, cycles, one-parameter continuum of periodic regimes, Hopf bifurcation, Preisach nonlinearity

Abstract

We survey a number of recent results and suggest some new ones on periodic solutions of systems with hysteresis. The main focus of this work is the situation when simple one-parameter structures of periodic regimes appear. We consider forced oscillations, cycles of autonomous systems and Hopf bifurcations from the equilibrium and from infinity.

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