Bifurcations and chaos control in discrete small-world networks

doi:10.1088/1674-1056/21/1/010503

中国物理B ›› 2012, Vol. 21 ›› Issue (1): 10503-010503.doi: 10.1088/1674-1056/21/1/010503

Bifurcations and chaos control in discrete small-world networks

孙海义¹, 李宁², 张庆灵²

(1)College of Science, Shenyang Jianzhu University, Shenyang 110168, China; (2)Institute of Systems Science, Northeastern University, Shenyang 110819, China

收稿日期:2011-05-25 修回日期:2011-08-12 出版日期:2012-01-15 发布日期:2012-01-20
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 60974004) and the Science Foundation of Ministry of Housing and Urban-Rural Development, China (Grant No. 2011-K5-31).

Bifurcations and chaos control in discrete small-world networks

Li Ning(李宁)^a), Sun Hai-Yi(孙海义)^b)†, and Zhang Qing-Ling(张庆灵)^a)

^a Institute of Systems Science, Northeastern University, Shenyang 110819, China; ^b College of Science, Shenyang Jianzhu University, Shenyang 110168, China

Received:2011-05-25 Revised:2011-08-12 Online:2012-01-15 Published:2012-01-20
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 60974004) and the Science Foundation of Ministry of Housing and Urban-Rural Development, China (Grant No. 2011-K5-31).

摘要/Abstract

摘要： An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed. The control method is then applied to a discrete small-world network model. Qualitative analyses and simulations show that under a generic condition, the bifurcations and the chaos can be delayed or eliminated completely. In addition, the periodic orbits embedded in the chaotic attractor can be stabilized.

关键词: bifurcation, chaos, small-world networks, impulsive delayed feedback control

Abstract: An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed. The control method is then applied to a discrete small-world network model. Qualitative analyses and simulations show that under a generic condition, the bifurcations and the chaos can be delayed or eliminated completely. In addition, the periodic orbits embedded in the chaotic attractor can be stabilized.

Key words: bifurcation, chaos, small-world networks, impulsive delayed feedback control

中图分类号: (Low-dimensional chaos)

05.45.Ac

05.45.Gg (Control of chaos, applications of chaos)

李宁, 孙海义, 张庆灵. Bifurcations and chaos control in discrete small-world networks[J]. 中国物理B, 2012, 21(1): 10503-010503.

Li Ning(李宁), Sun Hai-Yi(孙海义), and Zhang Qing-Ling(张庆灵) . Bifurcations and chaos control in discrete small-world networks[J]. Chin. Phys. B, 2012, 21(1): 10503-010503.

参考文献 30

[1]	Newman M E J and Watts D J 1999 Phys. Rev. E 60 7332
[2]	Moukarzel C F 1999 Phys. Rev. E 60 6263
[3]	Newman M E J, Morre C and Watts D J 2000 Phys. Rev. Lett. 84 3201
[4]	Watts D J 1999 Small-Worlds: The Dynamics of Networks Between Order and Randomness (Princeton, NJ: Princeton University Press)
[5]	Yang X S 2001 Phys. Rev. E 63 046206
[6]	Watts D J and Strogatz S H 1998 Nature 393 440
[7]	Li C G and Chen G R 2004 Chaos, Solitons Fractals 20 353
[8]	Chen Z, Zhao D H and Ruan J 2007 Chin. Ann. Math. 20 453
[9]	Ott E, Grebogi C and Yorke J A 1990 Phys. Rev. Lett. 64 1196
[10]	Luo X S, Chen G R, Wang B H, Fang J Q, Zou Y L and Quan H J 2003 Acta Phys. Sin. 52 790 (in Chinese)
[11]	Zhang R, Weng J Q, Luo X S and Fang J Q 2006 Chin. Phys. 15 1226
[12]	Zou Y L, Luo X S and Chen G R 2006 Chin. Phys. 15 1719
[13]	Liu Y Z, Jiang C S, Lin C S and Jiang Y M 2007 Chin. Phys. 16 660
[14]	Wang F Z, Chen Z Q, Wu W J and Yuan Z Z 2007 Chin. Phys. 16 3238
[15]	Li R H, Xu W and Li S 2007 Chin. Phys. 16 1591
[16]	Liu F, Guan Z H and Wang H 2008 Chin. Phys. B 17 2405
[17]	Tan P A, Zhang B and Qiu D Y 2010 Acta Phys. Sin. 59 5299 (in Chinese)
[18]	Pyragas K 1992 Phys. Lett. A 170 421
[19]	Ushio T 1996 IEEE Trans. Circ. Syst. I 43 815
[20]	Morgül Ö 2003 Phys. Lett. A 314 278
[21]	Socolar J E, Sukow D W and Gauthier D J 1994 Phys. Rev. E 50 3245
[22]	Kittel A, Parisi J and Pyragas K 1995 Phys. Lett. A 198 433
[23]	Pyragas K 1995 Phys. Lett. A 206 323
[24]	Pyragas K 2001 Phys. Rev. Lett. 86 2265
[25]	Schuster H G and Stemmler M B 1997 Phys. Rev. E 56 6410
[26]	Morgül Ö 2006 Int. J. Bifurcation Chaos 16 311
[27]	Morgül Ö 2007 Int. J. Bifurcation Chaos 17 4431
[28]	Wu S H, Hao J H and Xu H B 2010 Chin. Phys. B 19 020509
[29]	Morgül Ö 2009 Int. J. Bifurcation Chaos 19 365
[30]	Lin W, Ma H F, Feng J F and Chen G R 2010 Phys. Rev. E 82 046214

Bifurcations and chaos control in discrete small-world networks

Bifurcations and chaos control in discrete small-world networks

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