WIAS Preprint No. 902, (2004)

Asymptotic stability of continual sets of periodic solutions to systems with hysteresis


  • Brokate, Martin
  • Pokrovskii, Alexei
  • Rachinskii, Dmitri

2010 Mathematics Subject Classification

  • 34C55 34D20 34D10


  • Hysteresis perturbations of ODE, Preisach hysteresis nonlinearity, periodic solutions, stability


We consider hysteresis perturbations of the system of ODEs which has an asymptotically stable periodic solution $z_*$. It is proved that if the oscillation of the appropriate projection of $z_*$ is smaller than some threshold number defined by the hysteresis nonlinearity, then the perturbed system has a continuum of periodic solutions with a rather simple structure in a vicinity of $z_*$. The main result is the theorem on stability of this continuum.

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