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By use of a new variable, the original three-dimensional system transforms into an equivalent four-dimensional system. Firstly, we study the existence and local stability of positive equilibrium of the new system. And, by choosing the time delay<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>\u03c4<\/mml:mi><\/mml:mrow><\/mml:math>as a bifurcation parameter, we show that Hopf bifurcation may occur as the time delay<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>\u03c4<\/mml:mi><\/mml:mrow><\/mml:math>passes through some critical values. Secondly, by use of normal form theory and central manifold argument, we establish the direction and stability of Hopf bifurcation. At last, some simple discussion is presented.<\/jats:p>","DOI":"10.1155\/2013\/201936","type":"journal-article","created":{"date-parts":[[2013,11,3]],"date-time":"2013-11-03T16:00:51Z","timestamp":1383494451000},"page":"1-10","source":"Crossref","is-referenced-by-count":2,"title":["Stability and Hopf Bifurcation Analysis for a Stage-Structured Predator-Prey Model with Discrete and Distributed Delays"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7012-7651","authenticated-orcid":true,"given":"Ruiqing","family":"Shi","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China"},{"name":"School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junmei","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, 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