Periodic solutions of isotone hybrid systems

Abstract

Suggested by conversations in 1991 (Mark~Krasnosel'ski\u{\i} and Aleksei~Pokrovski\u{\i} with TIS), this paper generalizes earlier work (Krasnosel'ski\u{\i}-Pokrovski\u{\i} 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