{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:45Z","timestamp":1740134565986,"version":"3.37.3"},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11026189","ZR2010AQ021"],"award-info":[{"award-number":["11026189","ZR2010AQ021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of Shandong Province","award":["11026189","ZR2010AQ021"],"award-info":[{"award-number":["11026189","ZR2010AQ021"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We consider a complex autonomously driven single limit cycle oscillator with delayed feedback. The original model is translated to a two-dimensional system. Through a nonstandard finite-difference (NSFD) scheme we study the dynamics of this resulting system. The stability of the equilibrium of the model is investigated by analyzing the characteristic equation. In the two-dimensional discrete model, we find that there are stability switches on the time delay and Hopf bifurcation when the delay passes a sequence of critical values. Finally, computer simulations are performed to illustrate the theoretical results. And the results show that NSFD scheme is better than the Euler method.<\/jats:p>","DOI":"10.1155\/2013\/912374","type":"journal-article","created":{"date-parts":[[2013,7,24]],"date-time":"2013-07-24T19:34:05Z","timestamp":1374694445000},"page":"1-11","source":"Crossref","is-referenced-by-count":0,"title":["Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback"],"prefix":"10.1155","volume":"2013","author":[{"given":"Yuanyuan","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China"},{"name":"School of Science, China University of Petroleum (East China), Qingdao 266555, China"}]},{"given":"Xiaohua","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(00)00086-5"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.05.028"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1080\/00207160903201716"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2008.03.044"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2012.02.023"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2009.04.008"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.12.013"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.074"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.06.073"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(02)00546-5"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.05.055"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.11.046"},{"issue":"1-2","key":"13","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1016\/S0377-0427(99)00181-8","volume":"115","year":"2000","journal-title":"Journal of Computational and Applied Mathematics"},{"year":"1999","key":"14"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(02)00223-4"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1080\/10236190500127471"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1080\/10236198.2011.574622"},{"year":"1995","key":"18"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2004.07.027"},{"issue":"6","key":"19","first-page":"863","volume":"10","year":"2003","journal-title":"Dynamics of Continuous, Discrete & Impulsive Systems A"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/S1468-1218(01)00039-6"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/912374.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/912374.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/912374.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T12:45:48Z","timestamp":1498049148000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/912374\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":21,"alternative-id":["912374","912374"],"URL":"https:\/\/doi.org\/10.1155\/2013\/912374","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}