Periodic solutions of isotone hybrid systems
- Seidman, Thomas I.
- Klein, Olaf
2010 Mathematics Subject Classification
- 34K34 47J40 34A38 34C55 93C30
- Periodic, hybrid system, discontinuous, hysteresis, isotone, fixed point, calcium waves
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.
- Discrete Contin. Dyn. Syst. Ser. B, 18 (2013) pp. 483--493.