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Firstly, local stability of equilibrium indicating the extinction of top\u2010predator is obtained. Meanwhile, we construct a Lyapunov function, which is an extension of the Lyapunov functions constructed by Hsu for predator\u2010prey system (2005), to give the global stability of the equilibrium. Secondly, we analyze the stability of coexisting equilibrium of predator\u2010prey system with time delay when the predator catches the prey of pregnancy or with growth time. The delay can lead to periodic solutions, which is consistent with the law of growth for birds and some mammals. Further, an explicit formula is given which determines the stability of the bifurcating periodic solutions theoretically and the existence of periodic solutions is displayed by numerical simulations.<\/jats:p>","DOI":"10.1155\/2012\/260798","type":"journal-article","created":{"date-parts":[[2012,3,22]],"date-time":"2012-03-22T15:10:03Z","timestamp":1332429003000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Global Stability and Hopf Bifurcation for Gause\u2010Type Predator\u2010Prey System"],"prefix":"10.1155","volume":"2012","author":[{"given":"Shuang","family":"Guo","sequence":"first","affiliation":[]},{"given":"Weihua","family":"Jiang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,3,20]]},"reference":[{"volume-title":"Deterministic Mathematical Models in Population Ecology","year":"1980","author":"Freedman H. 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