{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T01:17:11Z","timestamp":1649207831584},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,11]]},"abstract":"<jats:p> We consider dynamical systems on time domains that alternate between continuous time intervals and discrete time intervals. The dynamics on the continuous portions may represent species growth when there is population overlap and are governed by differential or partial differential equations. The dynamics across the discrete time intervals are governed by a chaotic map and may represent population growth which is seasonal. We study the long term dynamics of this combined system. We study various conditions on the continuous time dynamics and discrete time dynamics that produce chaos and alternatively nonchaos for the combined system. When the discrete system alone is chaotic we provide a condition on the continuous dynamical component such that the combined system behaves chaotically. We also provide a condition that ensures that if the discrete time system has an absolutely continuous invariant measure so will the combined system. An example based on the logistic continuous time and logistic discrete time component is worked out. <\/jats:p>","DOI":"10.1142\/s0218127409025158","type":"journal-article","created":{"date-parts":[[2010,2,24]],"date-time":"2010-02-24T01:07:55Z","timestamp":1266973675000},"page":"3829-3832","source":"Crossref","is-referenced-by-count":0,"title":["CHAOS OF DYNAMICAL SYSTEMS ON GENERAL TIME DOMAINS"],"prefix":"10.1142","volume":"19","author":[{"given":"ABRAHAM","family":"BOYARSKY","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PAWE\u0141","family":"G\u00d3RA","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139174565"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0201-1"},{"key":"rf3","series-title":"Probability and its Applications","volume-title":"Laws of Chaos. Invariant Measures and Dynamical Systems in One Dimension","author":"Boyarsky A.","year":"1997"},{"key":"rf4","series-title":"Addison-Wesley Studies in Nonlinearity","volume-title":"A First Course in Chaotic Dynamical Systems. Theory and Experiment","author":"Devaney R. L.","year":"1992"},{"key":"rf5","unstructured":"M.\u00a0Misiurewicz, Absolutely Continuous Measures for Certain Maps of an Interval, Inst. Hautes \u00c9tudes Sci. Publ. Math. (1981)\u00a0pp. 17\u201351."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409025158","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:55:15Z","timestamp":1565135715000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409025158"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11]]},"references-count":5,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,11]]}},"alternative-id":["10.1142\/S0218127409025158"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409025158","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11]]}}}