Hopf bifurcation analysis of integro-differential equation with unbounded delay |
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| Authors: | Lan ZhangChengjian Zhang Dongming Zhao |
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| Affiliation: | a College of Electrical and Computer Engineering, University of Michigan-Dearborn, MI 48128, USA
b School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China |
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| Abstract: | The complexity of a nonlinear dynamical system is controllable via a selection of system parameters. One representative behavior of such a complex system can be illustrated by Hopf bifurcation. This paper presents a Hopf bifurcation analysis of a kind of integro-differential equations with unbounded delay. Based on the Hopf bifurcation principle, a set of relationships among system parameters are obtained when a periodic orbit exists in the system. A numerical analysis is applied to solve the integro-differential delay equation. This paper proves the existence of Hopf bifurcation in the corresponding difference equations under the same system parameters as that in the integro-differential delay equations. |
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| Keywords: | Integro-differential delay equation Hopf bifurcation Naimark-Sacker bifurcation θ-method |
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