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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 Name | Affiliation | | 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. |
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