Stability of Periodic Solutions for Hysteresis-Delay Differential Equations

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. © 2018 Springer Science+Business Media, LLC, part of Springer Nature

Authors
Gurevich P. 1, 2 , Ron E.3
Language
English
Pages
1-48
Status
Published
Year
2018
Organizations
  • 1 Free University of Berlin, Berlin, Germany
  • 2 RUDN University, Moscow, Russian Federation
  • 3 Cryptom Technologies, Berlin, Germany
Keywords
Delay; Hysteresis; Periodic orbits; Stability
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/6704/