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Hopf Bifurcation Analysis of a Class of Abstract Delay Differential Equation
  
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KeyWord:Hopf bifurcation; Delay; Stability; Normal form; Periodic solution
Author NameAffiliation
Fengyuan Zhong Department of Mathematics, Harbin University of Science and Technology, Harbin, Heilongjiang 150080, China 
Zicheng Xu College of Mathematical Sciences, Harbin Engineering University, Harbin, Heilongjiang 150001, China 
Bin Ge Department of Mathematics, Harbin University of Science and Technology, Harbin, Heilongjiang 150080, China 
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Abstract:
      The dynamics of a class of abstract delay differential equations are investigated. We prove that a sequence of Hopf bifurcations occur at the origin equilibrium as the delay increases. By using the theory of normal form and centre manifold, the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions is derived. Then, the existence of the global Hopf bifurcation of the system is discussed by applying the global Hopf bifurcation theorem of general functional differential equation.