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Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis.<\/jats:p>","DOI":"10.1155\/2012\/768364","type":"journal-article","created":{"date-parts":[[2012,12,4]],"date-time":"2012-12-04T22:12:21Z","timestamp":1354659141000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Hopf Bifurcation of a Differential\u2010Algebraic Bioeconomic Model with Time Delay"],"prefix":"10.1155","volume":"2012","author":[{"given":"Xiaojian","family":"Zhou","sequence":"first","affiliation":[]},{"given":"Xin","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Yongzhong","family":"Song","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,12,4]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.2307\/1934339"},{"key":"e_1_2_5_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.06.056"},{"volume-title":"Theory and Applications of Hopf Bifurcation","year":"1981","author":"Hassard B. 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