Delay induced Hopf bifurcation of small-world networks

被引：5

作者：

Chen, Zhang ^{[1
]}

Zhao, Donghua

Ruan, Jiong

机构：

[1] Shandong Univ, Sch Math & Syst Sci, Jinan 250100, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Fudan Univ, Lab Math & Nonlinear Sci, Shanghai 200433, Peoples R China

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2007年 / 28卷 / 04期

关键词：

small-world networks; time delay; Hopf bifurcation;

D O I：

10.1007/s11401-005-0300-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：453 / 462

页数：10

共 50 条

[1] Delay Induced Hopf Bifurcation of Small-World Networks [J].

Zhang Chen ;

Donghua Zhao ;

Jiong Ruan .

Chinese Annals of Mathematics, Series B, 2007, 28 :453-462

[2] Delay Induced Hopf Bifurcation of Small-World Networks [J].

Zhang CHEN Donghua ZHAO Jiong RUAN School of Mathematics and System SciencesShandong UniversityJinan China School of Mathematical Sciences and Laboratory of Mathematics for Nonlinear SciencesFudan UniversityShanghai China .

ChineseAnnalsofMathematics, 2007, (04) :453-462

[3] Delay Induced Hopf Bifurcation in a Small-world Network Model [J].

Ma, Li-Na ;

Geng, Meng-Ya ;

Wang, Han ;

Ding, Da-Wei .

INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND COMMUNICATION ENGINEERING (CSCE 2015), 2015, :1061-1068

[4] Hopf Bifurcation of Fractional-Order Small-World Networks with Time Delay [J].

Zhu Fanchao ;

Xiao Min ;

Tao Binbin .

PROCEEDINGS OF THE 30TH CHINESE CONTROL AND DECISION CONFERENCE (2018 CCDC), 2018, :2370-2375

[5] Hybrid Control of Delay Induced Hopf Bifurcation of Dynamical Small-World Network [J].

丁大为 ;

张肖芸 ;

王年 ;

梁栋 .

Journal of Shanghai Jiaotong University(Science), 2017, 22 (02) :206-215

[6] Hybrid control of delay induced hopf bifurcation of dynamical small-world network [J].

Ding D. ;

Zhang X. ;

Wang N. ;

Liang D. .

Journal of Shanghai Jiaotong University (Science), 2017, 22 (02) :206-215

[7] Hopf bifurcation for a small-world network model with parameters delay feedback control [J].

Hongyong Zhao ;

Wen Xie .

Nonlinear Dynamics, 2011, 63 :345-357

[8] Hopf bifurcation for a small-world network model with parameters delay feedback control [J].

Zhao, Hongyong ;

Xie, Wen .

NONLINEAR DYNAMICS, 2011, 63 (03) :345-357

[9] Bifurcation control in small-world networks [J].

Cheng, Zunshui ;

Cao, Jinde .

NEUROCOMPUTING, 2009, 72 (7-9) :1712-1718

[10] Time-delayed feedback control of dynamical small-world networks at Hopf bifurcation [J].

Xiao, Min ;

Ho, Daniel W. C. ;

Cao, Jinde .

NONLINEAR DYNAMICS, 2009, 58 (1-2) :319-344

← 1 2 3 4 5 →