Delay Systems Global Existence of Hopf bifurcation 

 :783-790. WenXianzhang, WangZhicheng. TheExistenceofPeriodicSolutionsforSomeModelswithDelay [J]. NolinearAnalysi8: RealWorldApplications, 2002 (3) :567-581. WuJianhong. TheoryandApplicationsofPartialFunctionalDifferentialEquations [M]. NewYork: Spring. Verlag, 1996. WangWendi, MaZhi'en. HarmlessDelayforUniformPersistence [J]. JmathAnaApp1, 1991,158 (1) :256-268. WuJianhong. SymmetricFunctionalDifferentialEquationsandNeuralNetworkswithMemory [J]. TransAmmerMathSoc. 1998.198:4799-4838. [Responsibility Editing: Zhang Yongjun] TheExistenceofGlobalHopeBifurcationforaPedator-PreySystemwithDelayWEIZhang-zhi, ZHANGZu. feng,herve leger skirts, WANGLiang. 1ong (1.SchoolofMathematicsandComputationalScience, AnhuiUniversity, Hefei230039; 2.DepartmentofMathematics, SuzhouCollege, Suzhou,vibram five fingers kso, Anhui234000,mbt zapatos, China) Abstract: Thispaperconsidersthestabilityandlocalbifurcationasadelaypredator. preysystemwhenrateregardingasaparamter, combiningtheglobalHopfbifurcationtheoremforgeneralfunctionaldifferentialequations, andweinvestigatetheexistenceofglobalHopfbifurcation. Keywords: delay; stability; localHopfbifurcation; globalHopfbifurcation recognized by the international mathematical community named after the Chinese mathematical research (10) Wang Theorem: Wang Shu-Tang on the point set topology of the research results. Wangcheng Tang (1933 a), Hebei Hejian people; Northwestern University Professor of Mathematics. famous quote and comment topologists, and was known as Lemma Yuan: Yuan Yaxiang nonlinear planning research. Yuan Yaxiang (1960 a), Hunan Zixing people; Computational Mathematics and Scientific Engineering Computing, Institute Fellow, Academy of Mathematics and Systems Science Institute. Non-linear planning in his research is internationally named King's Operator: Huan Jing is a symmetric function in terms of research results. King is Huan (1962 a), Hubei Wuhan; Chinese-American, the famous generation of mathematicians, North Carolina State University. He is mainly engaged in infinite-dimensional Lie algebra, representation theory of quantum groups and the research work. Frenkel the first time he and co-construction of quantum affine vertex algebra that is entirely constructed around the vertices of type affine quantum algebra said. The introduction of vertex operator method SchurQ one, Hall-Litflewood other symmetric polynomial function, and promote an infinite dimensional Lie algebra and algebraic combinations of the crossover study, 

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