{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T15:56:53Z","timestamp":1773158213161,"version":"3.50.1"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11361046"],"award-info":[{"award-number":["11361046"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Science and Technology Pillar Program of Ningxia","award":["KJ[2015]26(4)"],"award-info":[{"award-number":["KJ[2015]26(4)"]}]},{"name":"the key Program of Higher Education of Henan","award":["16A110038"],"award-info":[{"award-number":["16A110038"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,6,15]]},"abstract":"<jats:p>We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.<\/jats:p>","DOI":"10.1142\/s0218127416501054","type":"journal-article","created":{"date-parts":[[2016,6,29]],"date-time":"2016-06-29T06:02:54Z","timestamp":1467180174000},"page":"1650105","source":"Crossref","is-referenced-by-count":17,"title":["Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback"],"prefix":"10.1142","volume":"26","author":[{"given":"Jihua","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Ningxia Normal University, Xueyuan Rd., Guyuan 756000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erli","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Zhengzhou Institute of Finance and Economics, Tianhe Rd. 36, Zhengzhou 475000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mei","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Ningxia Normal University, Xueyuan Rd., Guyuan 756000, P. R. China"},{"name":"Department of Information Engineering, Zhengzhou Institute of Finance and Economics, Tianhe Rd. 36, Zhengzhou 475000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,6,28]]},"reference":[{"key":"S0218127416501054BIB001","doi-asserted-by":"crossref","first-page":"6268","DOI":"10.1016\/j.amc.2012.12.043","volume":"21","author":"Berezansky L.","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"S0218127416501054BIB002","doi-asserted-by":"publisher","DOI":"10.1063\/1.3085954"},{"key":"S0218127416501054BIB003","first-page":"901014","volume":"2013","author":"Bianca C.","year":"2013","journal-title":"Abstr. Appl. Anal."},{"key":"S0218127416501054BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.044"},{"key":"S0218127416501054BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1578-8"},{"key":"S0218127416501054BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.08.218"},{"key":"S0218127416501054BIB007","first-page":"59","volume":"8","author":"Ding J.","year":"2009","journal-title":"Int. J. Nonlin. Sci."},{"key":"S0218127416501054BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.07.036"},{"key":"S0218127416501054BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-009-9472-5"},{"key":"S0218127416501054BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.05.058"},{"key":"S0218127416501054BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2012.10.009"},{"key":"S0218127416501054BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9892-2"},{"key":"S0218127416501054BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.07.027"},{"key":"S0218127416501054BIB014","volume-title":"Theory and Applications of Hopf Bifurcation","author":"Hassard B. D.","year":"1981"},{"key":"S0218127416501054BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.econmod.2009.07.016"},{"key":"S0218127416501054BIB016","volume-title":"The Theory of Matrices with Applications","author":"Lancaster P.","year":"1985"},{"key":"S0218127416501054BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(01)00121-7"},{"key":"S0218127416501054BIB018","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016313804297"},{"key":"S0218127416501054BIB019","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022806003937"},{"key":"S0218127416501054BIB020","first-page":"889","volume":"25","author":"Ma J. H.","year":"2004","journal-title":"Appl. Math. Mech."},{"key":"S0218127416501054BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-008-9108-8"},{"key":"S0218127416501054BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.05.029"},{"key":"S0218127416501054BIB023","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.1196"},{"key":"S0218127416501054BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(92)90745-8"},{"key":"S0218127416501054BIB026","first-page":"863","volume":"10","author":"Ruan S.","year":"2003","journal-title":"Dyn. Contin. Discr. Impuls. Syst. Ser. A: Math. Anal."},{"key":"S0218127416501054BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2011.01.010"},{"key":"S0218127416501054BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2003.12.075"},{"key":"S0218127416501054BIB029","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-011-0137-9"},{"key":"S0218127416501054BIB030","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.02.056"},{"key":"S0218127416501054BIB031","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.07.017"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127416501054","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,23]],"date-time":"2020-09-23T02:32:54Z","timestamp":1600828374000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127416501054"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,15]]},"references-count":30,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2016,6,28]]},"published-print":{"date-parts":[[2016,6,15]]}},"alternative-id":["10.1142\/S0218127416501054"],"URL":"https:\/\/doi.org\/10.1142\/s0218127416501054","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,15]]}}}