{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:25:09Z","timestamp":1740122709373,"version":"3.37.3"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T00:00:00Z","timestamp":1685577600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T00:00:00Z","timestamp":1685577600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Event Dyn Syst"],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s10626-023-00380-0","type":"journal-article","created":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T06:03:48Z","timestamp":1691647428000},"page":"161-179","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Dynamics of products of matrices in max algebra"],"prefix":"10.1007","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2434-4767","authenticated-orcid":false,"given":"Shrihari","family":"Sridharan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sachindranath","family":"Jayaraman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yogesh","family":"Kumar Prajapaty","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,8,10]]},"reference":[{"issue":"376","key":"380_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0024-3795(97)10057-X","volume":"275","author":"RB Bapat","year":"1998","unstructured":"Bapat RB (1998) A max version of the Perron-Fr\u00f6benius theorem. Linear Algebra Appl 275(376):3\u201318","journal-title":"Linear Algebra Appl"},{"key":"380_CR2","doi-asserted-by":"publisher","first-page":"964","DOI":"10.1137\/S0895479893251782","volume":"16","author":"RB Bapat","year":"1995","unstructured":"Bapat RB, Stanford DP, van den Driessche P (1995) Pattern properties and spectral inequalities in max algebra. SIAM J Matrix Anal Appl 16:964\u2013976","journal-title":"SIAM J Matrix Anal Appl"},{"key":"380_CR3","doi-asserted-by":"crossref","unstructured":"Berman A, Plemmons RJ (1994) Nonnegative matrices in the mathematical sciences 9, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA","DOI":"10.1137\/1.9781611971262"},{"key":"380_CR4","doi-asserted-by":"crossref","unstructured":"Butkovic P (2010) Max-linear Systems: Theory and Algorithms Springer Monographs in Mathematics 27","DOI":"10.1007\/978-1-84996-299-5"},{"key":"380_CR5","doi-asserted-by":"crossref","unstructured":"Elsner L, van den Driessche P (1999) On the power method in max algebra. Linear Algebra Appl 302(303):17\u201332","DOI":"10.1016\/S0024-3795(98)10171-4"},{"issue":"334","key":"380_CR6","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0024-3795(00)00062-8","volume":"332","author":"L Elsner","year":"2001","unstructured":"Elsner L, van den Driessche P (2001) Modifying the power method in max algebra. Linear Algebra Appl 332(334):3\u201313","journal-title":"Linear Algebra Appl"},{"key":"380_CR7","doi-asserted-by":"crossref","unstructured":"Gaubert S (1994) Rational series over dioids and discrete event systems. In: G. Cohen, J.P. Quadrat (Eds.), Proceedings of the 11th International conference on analysis and optimization of systems, Sophia- Antipolis, France, June 1994, Lecture Notes in Control and Information Sciences, 199, Springer, London, 1994, pp 247\u2013256","DOI":"10.1007\/BFb0033554"},{"key":"380_CR8","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/S0024-3795(00)00020-3","volume":"307","author":"M Gavalec","year":"2000","unstructured":"Gavalec M (2000) Linear matrix period in max-plus algebra. Linear Algebra Appl 307:167\u2013182","journal-title":"Linear Algebra Appl"},{"key":"380_CR9","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/S0166-218X(99)00174-2","volume":"100","author":"M Gavalec","year":"2000","unstructured":"Gavalec M (2000) Computing orbit period in max-min algebra. Discrete Appl Math 100:49\u201365","journal-title":"Discrete Appl Math"},{"key":"380_CR10","volume-title":"Max plus at work Princeton Series in Applied Mathematics","author":"B Heidergott","year":"2006","unstructured":"Heidergott B, Oldser GJ, van der Woude J (2006) Max plus at work Princeton Series in Applied Mathematics. Princeton University Press"},{"key":"380_CR11","doi-asserted-by":"publisher","first-page":"223","DOI":"10.17398\/2605-5686.37.2.223","volume":"37","author":"S Jayaraman","year":"2022","unstructured":"Jayaraman S, Prajapaty YK, Sridharan S (2022) Dynamics of products of nonnegative matrices. Extracta Math 37:223\u2013242","journal-title":"Extracta Math"},{"key":"380_CR12","doi-asserted-by":"crossref","unstructured":"Lemmens B, Nussbaum RD (2012) Nonlinear perron-frobenius theory. Cambridge Tracts in Mathematics 189, Cambridge University Press","DOI":"10.1017\/CBO9781139026079"},{"key":"380_CR13","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1016\/j.laa.2010.08.027","volume":"436","author":"RD Katz","year":"2012","unstructured":"Katz RD, Schneider H, Sergeev S (2012) On commuting matrices in max algebra and in classical nonnegative algebra. Linear Algebra Appl 436:276\u2013292","journal-title":"Linear Algebra Appl"},{"key":"380_CR14","doi-asserted-by":"crossref","unstructured":"Pang CT, Guu SM (2001) A note on the sequence of consecutive powers of a nonnegative matrix in max algebra. Linear Algebra Appl 330:209\u2013213","DOI":"10.1016\/S0024-3795(01)00253-1"},{"key":"380_CR15","doi-asserted-by":"crossref","unstructured":"Rosenblatt D (1957) On the graphs and asymptotic forms of finite Boolean relation matrices and stochastic matrices. Naval Res Logist Quart 4:151\u2013167","DOI":"10.1002\/nav.3800040206"},{"key":"380_CR16","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/S0024-3795(00)00013-6","volume":"307","author":"B de Schutter","year":"2000","unstructured":"de Schutter B (2000) On the ultimate behavior of the sequence of consecutive powers of a matrix in the max-plus algebra. Linear Algebra Appl 307:103\u2013117","journal-title":"Linear Algebra Appl"}],"container-title":["Discrete Event Dynamic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10626-023-00380-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10626-023-00380-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10626-023-00380-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T13:11:21Z","timestamp":1692709881000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10626-023-00380-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["380"],"URL":"https:\/\/doi.org\/10.1007\/s10626-023-00380-0","relation":{},"ISSN":["0924-6703","1573-7594"],"issn-type":[{"type":"print","value":"0924-6703"},{"type":"electronic","value":"1573-7594"}],"subject":[],"published":{"date-parts":[[2023,6]]},"assertion":[{"value":"6 July 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 August 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no conflict of interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}}]}}