| Delay Induced Hopf Bifurcation of Small-World Networks |
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| 作者姓名： | Zhang CHEN Donghua ZHAO Jiong RUAN |
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| 作者单位： | Zhang CHEN Donghua ZHAO Jiong RUAN School of Mathematics and System Sciences，Shandong University，Jinan 250100，China. School of Mathematical Sciences and Laboratory of Mathematics for Nonlinear Sciences，Fudan University，Shanghai 200433，China. |
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| 摘 要： | In this paper,the stability and the Hopf bifurcation of small-world networks with time delay are studied.By analyzing the change of delay,we obtain several sufficient conditions on stable and unstable properties.When the delay passes a critical value,a Hopf bifurcation may appear.Furthermore,the direction and the stability of bifurcating periodic solutions are investigated by the normal form theory and the center manifold reduction.At last,by numerical simulations,we further illustrate the effectiveness of theorems in this paper.
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| 关 键 词： | Hopf分歧 时滞 小世界网络 网络理论 |
| 收稿时间： | 15 July 2005 |
Delay Induced Hopf Bifurcation of Small-World Networks |
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| Zhang CHEN,Donghua ZHAO,Jiong RUAN.Delay Induced Hopf Bifurcation of Small-World Networks[J].Chinese Annals of Mathematics,Series B,2007,28(4):453-462. |
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| Authors: | Zhang CHEN Donghua ZHAO and Jiong RUAN |
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| Institution: | 1. School of Mathematics and System Sciences, Shandong University, Jinan 250100, China
2. School of Mathematical Sciences and Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, China |
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| Abstract: | In this paper,the stability and the Hopf bifurcation of small-world networks with time delay are studied.By analyzing the change of delay,we obtain several sufficient conditions on stable and unstable properties.When the delay passes a critical value,a Hopf bifurcation may appear.Furthermore,the direction and the stability of bifurcating periodic solutions are investigated by the normal form theory and the center manifold reduction.At last,by numerical simulations,we further illustrate the effectiveness of theorems in this paper. |
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| Keywords: | Small-world networks Time delay Hopf bifurcation |
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