Weierstraß-Institut für Angewandte Analysis und Stochastik Leibniz-Institut im Forschungsverbund Berlin e.V. Preprint ISSN 0946 – 8633 Periodic solutions of isotone hybrid systems Dedicated to the memory of A.V. Pokrovski˘ ı Thomas I. Seidman 1 , Olaf Klein 2 submitted: September 14, 2012 1 Department of Mathematics and Statistics, University of Maryland Baltimore County (UMBC), Baltimore MD 21250 USA E-mail: seidman@umbc.edu 2 Weierstrass Institute Mohrenstr. 39 10117 Berlin Germany E-Mail: Olaf.Klein@wias-berlin.de No. 1732 Berlin 2012 2010 Mathematics Subject Classification. 34K34 47J40 34A38 34C55 93C30 . Key words and phrases. Periodic, hybrid system, discontinuous, hysteresis, isotone, fixed point, calcium waves. The research of the first author has been partially supported by the National Science Foundation under the grant ECS-8814788 and by the U.S. Air Force Office of Scientific Research under the grant AFOSR-91-0008.