{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T09:04:24Z","timestamp":1750323864382,"version":"3.40.3"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030925505"},{"type":"electronic","value":"9783030925512"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-030-92551-2_15","type":"book-chapter","created":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T04:04:36Z","timestamp":1650341076000},"page":"233-252","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Existence and Non Existence of Limit Cycles in Boolean Networks"],"prefix":"10.1007","author":[{"given":"Lilian","family":"Salinas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis","family":"G\u00f3mez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julio","family":"Aracena","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,20]]},"reference":[{"key":"15_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.dam.2012.07.003","volume":"161","author":"J Aracena","year":"2013","unstructured":"Aracena J, G\u00f3mez L, Salinas L (2013) Limit cycles and update digraphs in Boolean networks. Discret Appl Math 161:1\u20132","journal-title":"Discret Appl Math"},{"key":"15_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.biosystems.2009.03.006","volume":"97","author":"J Aracena","year":"2009","unstructured":"Aracena J, Goles E, Moreira A, Salinas L (2009) On the robustness of update schedules in Boolean networks. Biosystems 97:1\u20138","journal-title":"Biosystems"},{"key":"15_CR3","doi-asserted-by":"crossref","unstructured":"Bridoux F, Gaze-Maillot C, Perrot K, Sen\u00e9 S (2020) Complexity of limit-cycle problems in boolean networks (2020). arXiv:2001.07391","DOI":"10.1007\/978-3-030-67731-2_10"},{"key":"15_CR4","doi-asserted-by":"crossref","unstructured":"Davidich MI, Bornholdt S (2008) Boolean network model predicts cell cycle sequence of fission yeast. PloS one 3(2):e1672","DOI":"10.1371\/journal.pone.0001672"},{"issue":"1\u20132","key":"15_CR5","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s10441-008-9029-x","volume":"56","author":"J Demongeot","year":"2008","unstructured":"Demongeot J, Elena A, Sen\u00e9 S (2008) Robustness in regulatory networks: a multi-disciplinary approach. Acta Biotheor 56(1\u20132):27\u201349","journal-title":"Acta Biotheor"},{"issue":"14","key":"15_CR6","doi-asserted-by":"publisher","first-page":"e124","DOI":"10.1093\/bioinformatics\/btl210","volume":"22","author":"A Faur\u00e9","year":"2006","unstructured":"Faur\u00e9 A, Naldi A, Chaouiya C, Thieffry D (2006) Dynamical analysis of a generic boolean model for the control of the mammalian cell cycle. Bioinformatics 22(14):e124\u2013e131","journal-title":"Bioinformatics"},{"key":"15_CR7","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1142\/S0218339000000109","volume":"8","author":"E Goles","year":"2000","unstructured":"Goles E, Hern\u00e1ndez G (2000) Dynamical behavior of Kauffman networks with and-or gates. J Biol Syst 8:151\u2013175","journal-title":"J Biol Syst"},{"key":"15_CR8","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1016\/j.aam.2011.11.009","volume":"48","author":"E Goles","year":"2012","unstructured":"Goles E, Noual M (2012) Disjunctive networks and update schedules. Adv Appl Math 48:646\u2013662","journal-title":"Adv Appl Math"},{"issue":"4","key":"15_CR9","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1137\/0603054","volume":"3","author":"E Goles","year":"1982","unstructured":"Goles E (1982) Fixed point behavior of threshold functions on a finite set. SIAM J Algebr Discrete Methods 3(4):529\u2013531","journal-title":"SIAM J Algebr Discrete Methods"},{"key":"15_CR10","doi-asserted-by":"crossref","unstructured":"Goles E, Montalva M, Ruz GA (2013) Deconstruction and dynamical robustness of regulatory networks: application to the yeast cell cycle networks. Bull Math Biol 75(6):939\u2013966","DOI":"10.1007\/s11538-012-9794-1"},{"key":"15_CR11","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.tcs.2014.09.010","volume":"559","author":"E Goles","year":"2014","unstructured":"Goles E, Montealegre P (2014) Computational complexity of threshold automata networks under different updating schemes. Theoret Comput Sci 559:3\u201319","journal-title":"Theoret Comput Sci"},{"issue":"2","key":"15_CR12","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0012-365X(80)90121-1","volume":"30","author":"E Goles","year":"1980","unstructured":"Goles E, Olivos J (1980) Periodic behaviour of generalized threshold functions. Discret Math 30(2):187\u2013189","journal-title":"Discret Math"},{"key":"15_CR13","unstructured":"G\u00f3mez L (2015) Dynamics of discrete networks with deterministic updates schedules. Application to genetic regulatory networks. PhD thesis in mathematical engineering, Universidad de Concepci\u00f3n, Concepci\u00f3n, Chile"},{"key":"15_CR14","doi-asserted-by":"crossref","unstructured":"Green DG, Leishman TG, Sadedin S (2007) The emergence of social consensus in Boolean networks. In: IEEE symposium on artificial life, 2007. ALIFE\u201907. IEEE, pp 402\u2013408","DOI":"10.1109\/ALIFE.2007.367823"},{"key":"15_CR15","unstructured":"Just W (2006) The steady state system problem is np-hard even for monotone quadratic boolean dynamical systems. Submitted to Annals of Combinatorics"},{"key":"15_CR16","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/0022-5193(69)90015-0","volume":"22","author":"SA Kauffman","year":"1969","unstructured":"Kauffman SA (1969) Metabolic stability and epigenesis in randomly connected nets. J Theor Biol 22:437\u2013467","journal-title":"J Theor Biol"},{"key":"15_CR17","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195079517.001.0001","volume-title":"The origins of order: self-organization and selection in evolution","author":"SA Kauffman","year":"1993","unstructured":"Kauffman SA (1993) The origins of order: self-organization and selection in evolution. Oxford University Press, New York"},{"key":"15_CR18","doi-asserted-by":"crossref","unstructured":"Macauley M, Mortveit HS (2009) Cycle equivalence of graph dynamical systems. Nonlinearity 22(2):421","DOI":"10.1088\/0951-7715\/22\/2\/010"},{"key":"15_CR19","doi-asserted-by":"crossref","unstructured":"Mortveit HS (2012) Limit cycle structure for block-sequential threshold systems. In: Cellular automata. Springer, pp 672\u2013678","DOI":"10.1007\/978-3-642-33350-7_69"},{"issue":"5","key":"15_CR20","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/BF00204771","volume":"60","author":"S Porat","year":"1989","unstructured":"Porat S (1989) Stability and looping in connectionist models with asymmetric weights. Biol Cybern 60(5):335\u2013344","journal-title":"Biol Cybern"},{"key":"15_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61607-5","volume-title":"Discrete iterations: a metric study","author":"F Robert","year":"1986","unstructured":"Robert F (1986) Discrete iterations: a metric study. Springer, Berlin"},{"key":"15_CR22","unstructured":"Robert F (1995) Les systemes dynamiques discrets, vol\u00a019. Springer Science & Business Media, Berlin"},{"key":"15_CR23","doi-asserted-by":"crossref","unstructured":"Ruz GA, Timmermann T, Barrera J, Goles E (2014) Neutral space analysis for a boolean network model of the fission yeast cell cycle network. Biol Res 47(1):64","DOI":"10.1186\/0717-6287-47-64"},{"key":"15_CR24","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1016\/0022-5193(73)90247-6","volume":"42","author":"R Thomas","year":"1973","unstructured":"Thomas R (1973) Boolean formalization of genetic control circuits. J Theor Biol 42:563\u2013585","journal-title":"J Theor Biol"},{"key":"15_CR25","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1007\/978-3-642-81703-8_24","volume":"9","author":"R Thomas","year":"1980","unstructured":"Thomas R (1980) On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations. Springer Ser Synergetics 9:180\u2013193","journal-title":"Springer Ser Synergetics"},{"key":"15_CR26","volume-title":"Digital systems: principles and applications","author":"R Tocci","year":"2001","unstructured":"Tocci R, Widmer N (2001) Digital systems: principles and applications, 7th edn. Prentice-Hall, Hoboken","edition":"7"}],"container-title":["Emergence, Complexity and Computation","Automata and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-92551-2_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T04:32:32Z","timestamp":1700454752000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-92551-2_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783030925505","9783030925512"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-92551-2_15","relation":{},"ISSN":["2194-7287","2194-7295"],"issn-type":[{"type":"print","value":"2194-7287"},{"type":"electronic","value":"2194-7295"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"20 April 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}