{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:43:02Z","timestamp":1740134582031,"version":"3.37.3"},"reference-count":24,"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":["61273070"],"award-info":[{"award-number":["61273070"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Jiangsu Higher Education Institutions","award":["61273070"],"award-info":[{"award-number":["61273070"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>A four-dimensional recurrent neural network with two delays is considered. The main result is given in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the zero equilibrium and existence of the Hopf bifurcation with respect to both delays are obtained by analyzing the distribution of the roots of the associated characteristic equation. In particular, explicit formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form theory and center manifold theory. Some numerical examples are also presented to verify the theoretical analysis.<\/jats:p>","DOI":"10.1155\/2013\/436254","type":"journal-article","created":{"date-parts":[[2013,11,21]],"date-time":"2013-11-21T17:10:30Z","timestamp":1385053830000},"page":"1-13","source":"Crossref","is-referenced-by-count":2,"title":["Hopf Bifurcation Analysis for a Four-Dimensional Recurrent Neural Network with Two Delays"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2879-4434","authenticated-orcid":true,"given":"Zizhen","family":"Zhang","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China"},{"name":"School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huizhong","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.3724\/SP.J.1004.2008.01291"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-2312(03)00384-9"},{"issue":"10","key":"3","first-page":"1197","volume":"20","year":"2005","journal-title":"Control and Decision"},{"issue":"2","key":"4","first-page":"272","volume":"30","year":"2009","journal-title":"Chinese Journal of Scientific Instrument"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2009.12.009"},{"issue":"5","key":"6","first-page":"622","volume":"35","year":"2009","journal-title":"Acta Automatica Sinica"},{"issue":"1","key":"7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S1874-1029(13)60001-4","volume":"39","year":"2013","journal-title":"Acta Automatica Sinica"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.3724\/SP.J.1004.2010.00174"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(99)00009-3"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2009.03.033"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2009.08.018"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2010.06.023"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2007.08.008"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/697630"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2013.03.016"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2012.01.008"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.01.001"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1109\/72.701178"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1109\/72.822523"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2009.03.052"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-012-0699-1"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2010.09.002"},{"volume":"41","year":"1981","key":"23"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-010-0383-x"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/436254.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/436254.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/436254.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T22:56:20Z","timestamp":1498085780000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/436254\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":24,"alternative-id":["436254","436254"],"URL":"https:\/\/doi.org\/10.1155\/2013\/436254","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}