@article{464816617a174880bdd3053e20b3527c,

title = "On limit cycles of monotone functions with symmetric connection graph",

abstract = "We study the length of the limit cycles of discrete monotone functions with symmetric connection graph. We construct a family of monotone functions such that the limit cycles are of maximum possible length, which is exponential in the number of variables. Furthermore, we prove for the class of monotone functions with more than two states and connection graph equal to a caterpillar that the length of the limit cycles is at most two. Finally, we give some exclusion results in arbitrary trees.",

keywords = "Discrete network, Graph, Monotone function",

author = "Julio Aracena and Jacques Demongeot and Eric Goles",

note = "Funding Information: ∗Corresponding author. Current address: Departamento de Ingenier=>a Matema=tica, Universidad de Concepcio=n, Chile. E-mail addresses: jaracena@ing-mat.udec.cl (J. Aracena), demongeot@imag.fr (J. Demongeot), egoles@dim.uchile.cl (E. Goles). 1Partially supported by French Cooperation and Fondation pour la Recherche Me=dicale. 2Partially supported by CONICYT PhD fellowships. 3Partially supported by CONICYT PhD fellowships. 4Partially supported by FONDAP program in Applied Mathematics.",

year = "2004",

month = aug,

day = "30",

doi = "10.1016/j.tcs.2004.03.010",

language = "English",

volume = "322",

pages = "237--244",

journal = "Theoretical Computer Science",

issn = "0304-3975",

publisher = "Elsevier",

number = "2",

}