{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T23:33:29Z","timestamp":1723246409950},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,12]]},"abstract":" In this paper, we report a common phenomenon observed in chaotic systems linked by time delay. Recently, the Lorenz chaotic system has been extended to the family of Lorenz systems which includes the Chen and L\u00fc systems. These three chaotic systems, corresponding to different sets of system parameter values, are topologically different. With the aid of numerical simulations, we have surprisingly found that a simple time delay, directly applied to one or more state variables, transforms the Lorenz system to the generalized Chen system or the generalized L\u00fc system without any parameter changes. The existence of this phenomenon has also been found in other known chaotic systems: the R\u00f6ssler system, the Chua's circuit and the 4-Liu system. This finding has shown a common characteristic of chaotic systems: a new chaotic \"branch\" can be created from a chaotic attractor by simply adding a time delay. <\/jats:p>","DOI":"10.1142\/s0218127406017129","type":"journal-article","created":{"date-parts":[[2007,2,23]],"date-time":"2007-02-23T09:49:07Z","timestamp":1172224147000},"page":"3727-3736","source":"Crossref","is-referenced-by-count":17,"title":["A COMMON PHENOMENON IN CHAOTIC SYSTEMS LINKED BY TIME DELAY"],"prefix":"10.1142","volume":"16","author":[{"given":"PEI","family":"YU","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario, N6A 5B7, Canada"}]},{"given":"FEI","family":"XU","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario, N6A 5B7, Canada"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Dynamical Analysis, Control and Synchronization of Lorenz Families","author":"Chen G. R.","year":"2003"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1986.1085869"},{"key":"rf3","first-page":"336","volume":"4","author":"Farmer J.","journal-title":"Physica D"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406016148"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.02.060"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.44.2374"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(92)90745-8"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(76)90101-8"},{"key":"rf10","first-page":"1","volume":"17","author":"Tian Y.","journal-title":"Physica D"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405011990"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404010989"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406014976"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/S1007-5704(02)00007-2"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127406017129","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:58:59Z","timestamp":1565189939000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127406017129"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,12]]},"references-count":14,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,12]]}},"alternative-id":["10.1142\/S0218127406017129"],"URL":"https:\/\/doi.org\/10.1142\/s0218127406017129","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,12]]}}}