{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:46:30Z","timestamp":1753886790627,"version":"3.41.2"},"reference-count":25,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,9,29]],"date-time":"2012-09-29T00:00:00Z","timestamp":1348876800000},"content-version":"vor","delay-in-days":272,"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":["11031002"],"award-info":[{"award-number":["11031002"]}],"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>The dynamics of a system of two semiconductor lasers, which are delay coupled via a passive relay within the synchronization manifold, are investigated. Depending on the coupling parameters, the system exhibits synchronized Hopf bifurcation and the stability switches as the delay varies. Employing the center manifold theorem and normal form method, an algorithm is derived for determining the Hopf bifurcation properties. Some numerical simulations are carried out to illustrate the analysis results.<\/jats:p>","DOI":"10.1155\/2012\/257635","type":"journal-article","created":{"date-parts":[[2012,10,1]],"date-time":"2012-10-01T04:05:10Z","timestamp":1349064310000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Synchronized Hopf Bifurcation Analysis in a Delay\u2010Coupled Semiconductor Lasers System"],"prefix":"10.1155","volume":"2012","author":[{"given":"Gang","family":"Zhu","sequence":"first","affiliation":[]},{"given":"Junjie","family":"Wei","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,9,29]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/2944.954133"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/3.910450"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1014212930111"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/040619958"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2005.06.016"},{"volume-title":"Retarded Dynamical Systems: Stability and Characteristic Functions","year":"1989","author":"St\u00e9p\u00e1n G.","key":"e_1_2_7_6_2"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.87.243901"},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.86.795"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-010-9908-y"},{"key":"e_1_2_7_10_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.5109"},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.62.011801"},{"key":"e_1_2_7_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.80.056205"},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2008.09.002"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.106.223901"},{"key":"e_1_2_7_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-009-9539-3"},{"key":"e_1_2_7_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-010-9733-3"},{"key":"e_1_2_7_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-008-9454-z"},{"key":"e_1_2_7_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-007-9299-x"},{"key":"e_1_2_7_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/JQE.1980.1070479"},{"key":"e_1_2_7_20_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.53.4429"},{"key":"e_1_2_7_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(82)90042-2"},{"key":"e_1_2_7_22_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.79.065201"},{"key":"e_1_2_7_23_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"},{"volume-title":"Theory and Applications of Hopf Bifurcation","year":"1981","author":"Hassard B. 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