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Journal of Dynamics and Differential Equations

, Volume 31, Issue 4, pp 1873–1920 | Cite as

Stability of Periodic Solutions for Hysteresis-Delay Differential Equations

  • Pavel GurevichEmail author
  • Eyal Ron
Article
  • 136 Downloads

Abstract

We study an interplay between delay and discontinuous hysteresis in dynamical systems. After having established existence and uniqueness of solutions, we focus on the analysis of stability of periodic solutions. The main object we study is a Poincaré map that is infinite-dimensional due to delay and non-differentiable due to hysteresis. We propose a general functional framework based on the fractional order Sobolev–Slobodeckij spaces and explicitly obtain a formal linearization of the Poincaré map in these spaces. Furthermore, we prove that the spectrum of this formal linearization determines the stability of the periodic solution and then reduce the spectral analysis to an equivalent finite-dimensional problem.

Keywords

Hysteresis Delay Periodic orbits Stability 

Notes

Acknowledgements

The research of the first author was supported by the DFG Heisenberg Programme (Grant No. GU 1482/1-2) and the RUDN University Program 5-100. Both authors acknowledge the support of the DFG project SFB 910.

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Copyright information

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Authors and Affiliations

  1. 1.Free University of BerlinBerlinGermany
  2. 2.RUDN UniversityMoscowRussia
  3. 3.Cryptom TechnologiesBerlinGermany

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