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.