{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:36:04Z","timestamp":1753886164938,"version":"3.41.2"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,1,18]],"date-time":"2012-01-18T00:00:00Z","timestamp":1326844800000},"content-version":"vor","delay-in-days":17,"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>We consider the nonlinear dynamical behavior of a\nthree\u2010dimensional recurrent neural network with time delay. By choosing the\ntime delay as a bifurcation parameter, we prove that Hopf bifurcation occurs\nwhen the delay passes through a sequence of critical values. Applying the nor\u2010\nmal form method and center manifold theory, we obtain some local bifurcation\nresults and derive formulas for determining the bifurcation direction and the\nstability of the bifurcated periodic solution. Some numerical examples are also\npresented to verify the theoretical analysis.<\/jats:p>","DOI":"10.1155\/2012\/357382","type":"journal-article","created":{"date-parts":[[2012,1,18]],"date-time":"2012-01-18T21:02:10Z","timestamp":1326920530000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Stability and Bifurcation Analysis of a Three\u2010Dimensional Recurrent Neural Network with Time Delay"],"prefix":"10.1155","volume":"2012","author":[{"given":"Yingguo","family":"Li","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,1,18]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.81.10.3088"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2007.912321"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2004.11.030"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2010.06.023"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/72.701178"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(00)00132-6"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(99)00009-3"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(95)00203-0"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2006.03.014"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.10.012"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2006.08.008"},{"volume-title":"Theory and Applications of Hopf Bifurcation","year":"1981","author":"Hassard B.","key":"e_1_2_6_12_2"},{"key":"e_1_2_6_13_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. Series A. 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