{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:29:50Z","timestamp":1759940990311,"version":"3.41.2"},"reference-count":11,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,1,19]],"date-time":"2012-01-19T00:00:00Z","timestamp":1326931200000},"content-version":"vor","delay-in-days":18,"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":["10871056"],"award-info":[{"award-number":["10871056"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We analyze a differential\u2010algebraic biological economic system with time delay. The model has two different Holling functional responses. By considering time delay as bifurcation parameter, we find that there exists stability switches when delay varies, and the Hopf bifurcation occurs when delay passes through a sequence of critical values. Furthermore, we also consider the stability and direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, using Matlab software, we do some numerical simulations to illustrate the effectiveness of our results.<\/jats:p>","DOI":"10.1155\/2012\/205346","type":"journal-article","created":{"date-parts":[[2012,1,19]],"date-time":"2012-01-19T21:03:43Z","timestamp":1327007023000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Dynamic Properties of a Differential\u2010Algebraic Biological Economic System"],"prefix":"10.1155","volume":"2012","author":[{"given":"Hongyang","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Chunrui","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,1,19]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2005.851396"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2004.832741"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(00)00033-X"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.03.126"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-004-0278-2"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.05.025"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00226-1"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2004.12.011"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1086\/257497"},{"key":"e_1_2_6_10_2","first-page":"429","article-title":"Normal forms and bifurcations for differential-algebraic systems","volume":"23","author":"Chen B. S.","year":"2000","journal-title":"Acta Mathematicae Applicatae Sinica"},{"volume-title":"Theory and Applications of Hopf Bifurcation","year":"1981","author":"Hassard B. D.","key":"e_1_2_6_11_2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/205346.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/205346.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/205346","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:59:55Z","timestamp":1718089195000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/205346"}},"subtitle":[],"editor":[{"given":"Wan-Tong","family":"Li","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/205346"],"URL":"https:\/\/doi.org\/10.1155\/2012\/205346","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-08-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-10-04","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-01-19","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"205346"}}