WIAS Preprint No. 1732, (2012)

Periodic solutions of isotone hybrid systems



Authors

  • Seidman, Thomas I.
  • Klein, Olaf
    ORCID: 0000-0002-4142-3603

2010 Mathematics Subject Classification

  • 34K34 47J40 34A38 34C55 93C30

Keywords

  • Periodic, hybrid system, discontinuous, hysteresis, isotone, fixed point, calcium waves

Abstract

Suggested by conversations in 1991 (Mark Krasnosel'skiĭ and Aleksei Pokrovskiĭ with TIS), this paper generalizes earlier work (Krasnosel'skiĭ-Pokrovskiĭ 1974) of theirs by defining a setting of hybrid systems with isotone switching rules for a partially ordered set of modes and then obtaining a periodicity result in that context. An application is given to a partial differential equation modeling calcium release and diffusion in cardiac cells.

Appeared in

  • Discrete Contin. Dyn. Syst. Ser. B, 18 (2013) pp. 483--493.

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