{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:52:16Z","timestamp":1772293936281,"version":"3.50.1"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,4,5]],"date-time":"2012-04-05T00:00:00Z","timestamp":1333584000000},"content-version":"vor","delay-in-days":95,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"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>A kind of nonlinear finance system with time\u2010delayed feedback is considered. \nFirstly, by employing the polynomial theorem to analyze the distribution\nof the roots to the associate characteristic equation, the conditions\nof ensuring the existence of Hopf bifurcation are given. Secondly, by using\nthe normal form theory and center manifold argument, we derive the explicit\nformulas determining the stability, direction, and other properties of bifurcating\nperiodic solutions. Finally, we give several numerical simulations, which\nindicate that when the delay passes through certain critical values, chaotic\noscillation is converted into a stable steady state or a stable periodic orbit.<\/jats:p>","DOI":"10.1155\/2012\/316390","type":"journal-article","created":{"date-parts":[[2012,4,5]],"date-time":"2012-04-05T21:17:52Z","timestamp":1333660672000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos"],"prefix":"10.1155","volume":"2012","author":[{"given":"Rongyan","family":"Zhang","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016313804297"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022806003937"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02438345"},{"key":"e_1_2_6_4_2","first-page":"59","article-title":"A new modified hyperchaotic finance system and its control","volume":"8","author":"Ding J.","year":"2009","journal-title":"International Journal of Nonlinear Science"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.10.016"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-009-9472-5"},{"key":"e_1_2_6_7_2","first-page":"1","article-title":"Chaos and Hopf bifurcation of a finance system with distributed time delay","volume":"6","author":"Wang Y.","year":"2010","journal-title":"International Journal of Applied Mathematics and Mechanics"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2011.01.010"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.1196"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(92)90745-8"},{"key":"e_1_2_6_11_2","series-title":"Texts in Applied Mathematics","volume-title":"Introduction to Applied Nonlinear Dynamical Systems and Chaos","author":"Wiggins S.","year":"2003"},{"key":"e_1_2_6_12_2","first-page":"863","article-title":"On the zeros of transcendental functions with applications to stability of delay differential equations with two delays","volume":"10","author":"Ruan S.","year":"2003","journal-title":"Dynamics of Continuous, Discrete & Impulsive Systems A"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2003.12.075"},{"key":"e_1_2_6_14_2","series-title":"London Mathematical Society Lecture Note Series","volume-title":"Theory and Applications of Hopf Bifurcation","author":"Hassard B. D.","year":"1981"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/316390.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/316390.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/316390","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:47:52Z","timestamp":1718088472000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/316390"}},"subtitle":[],"editor":[{"given":"Chuanhou","family":"Gao","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/316390"],"URL":"https:\/\/doi.org\/10.1155\/2012\/316390","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-10-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-01-23","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-04-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"316390"}}