Control schemes for synchronizing two subnetworks with weak couplings

doi:10.1088/1674-1056/23/1/010507

Abstract In this paper, we propose a well-designed network model with a parameter and study full and partial synchronization of the network model based on the stability analysis. The network model is composed of a star-coupled subnetwork and a globally coupled subnetwork. By analyzing the special coupling configuration, three control schemes are obtained for synchronizing the network model. Further analysis indicates that even if the inner couplings in each subnetwork are very weak, two of the control schemes are still valid. In particular, if the outer coupling weight parameter θ is larger than (n²-2n)/4, or the subnetwork size n is larger than θ², the two subnetworks with weak inner couplings can achieve synchronization. In addition, the synchronizability is independent of the network size in case of 0< θ < n/(n+1). Finally, we carry out some numerical simulations to confirm the validity of the obtained control schemes. It is worth noting that the main idea of this paper also applies to any network consisting of a dense subnetwork and a sparse network.

Keywords: synchronization weak coupling star-global network control scheme

Received: 12 June 2013
Revised: 02 July 2013
Accepted manuscript online:

PACS:	05.45.Xt	(Synchronization; coupled oscillators)
	05.45.Gg	(Control of chaos, applications of chaos)
	89.75.-k	(Complex systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11162004, 10972011, and 11001069), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LQ12A01003 and LQ12A01002), and the Science Foundation of Guangxi Province, China (Grant No. 2013GXNSFAA019006).

Corresponding Authors: Ma Zhong-Jun
E-mail: mzj1234402@163.com

Cite this article:

Zhang Jian-Bao (张建宝), Ma Zhong-Jun (马忠军), Zhang Gang (张刚) Control schemes for synchronizing two subnetworks with weak couplings 2014 Chin. Phys. B 23 010507

[1]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[2]	Pecora L M and Carroll T L 1998 Phys. Rev. Lett. 80 2109
[3]	Wu W and Chen T P 2009 Physica D 238 355
[4]	Huang J J, Li C D, Zhang W and Wei P C 2012 Chin. Phys. B 21 090508
[5]	Yu H T, Wang J, Deng B and Wei X L 2013 Chin. Phys. B 22 018701
[6]	Liu B, Lu W L and Chen T P 2012 Neural Networks 25 5
[7]	Wu J S, Jiao L C and Chen G R 2011 Chin. Phys. B 20 060503
[8]	Zhang X F, Chen X K and Bi Q S 2013 Acta Phys. Sin. 62 010502 (in Chinese)
[9]	Feng C, Zou Y L and Wei F Q 2013 Acta Phys. Sin. 62 070506 (in Chinese)
[10]	Wu X Q, Zheng W X and Zhou J 2009 Chaos 19 013109
[11]	Ma Z J, Zhang S Z, Jiang G R and Li K Z 2013 Nonlinear Dynam. 74 55
[12]	Belykh V N, Belykh I V and Hasler M 2000 Phys. Rev. E 62 6332
[13]	Golubitsky M and Stewart I 2006 Bull. Amer. Math. Soc. 43 305
[14]	Wu C W and Chua L O 1995 IEEE Trans. CAS-I 42 430
[15]	Lu W L and Chen T P 2006 Physica D 213 214
[16]	Ma Z J, Liu Z R and Zhang G 2006 Chaos 16 023103
[17]	Belykh V N, Belykh I V, Nevidin K and Hasler M 2003 Chaos 13 165
[18]	Liu X W and Chen T P 2008 Physica D 237 630
[19]	Heagy J F, Pecora L M and Carroll T L 1995 Phys. Rev. Lett. 74 4185
[20]	Pogromsky A Y, Santoboni G and Nijmeijer H 2003 Nonlinearity 16 1597

[1]	Diffusive field coupling-induced synchronization between neural circuits under energy balance Ya Wang(王亚), Guoping Sun(孙国平), and Guodong Ren(任国栋). Chin. Phys. B, 2023, 32(4): 040504.
[2]	Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Chin. Phys. B, 2023, 32(3): 038701.
[3]	Influence of coupling asymmetry on signal amplification in a three-node motif Xiaoming Liang(梁晓明), Chao Fang(方超), Xiyun Zhang(张希昀), and Huaping Lü(吕华平). Chin. Phys. B, 2023, 32(1): 010504.
[4]	Power-law statistics of synchronous transition in inhibitory neuronal networks Lei Tao(陶蕾) and Sheng-Jun Wang(王圣军). Chin. Phys. B, 2022, 31(8): 080505.
[5]	Effect of astrocyte on synchronization of thermosensitive neuron-astrocyte minimum system Yi-Xuan Shan(单仪萱), Hui-Lan Yang(杨惠兰), Hong-Bin Wang(王宏斌), Shuai Zhang(张帅), Ying Li(李颖), and Gui-Zhi Xu(徐桂芝). Chin. Phys. B, 2022, 31(8): 080507.
[6]	Multi-target ranging using an optical reservoir computing approach in the laterally coupled semiconductor lasers with self-feedback Dong-Zhou Zhong(钟东洲), Zhe Xu(徐喆), Ya-Lan Hu(胡亚兰), Ke-Ke Zhao(赵可可), Jin-Bo Zhang(张金波),Peng Hou(侯鹏), Wan-An Deng(邓万安), and Jiang-Tao Xi(习江涛). Chin. Phys. B, 2022, 31(7): 074205.
[7]	Synchronization of nanowire-based spin Hall nano-oscillators Biao Jiang(姜彪), Wen-Jun Zhang(张文君), Mehran Khan Alam, Shu-Yun Yu(于淑云), Guang-Bing Han(韩广兵), Guo-Lei Liu(刘国磊), Shi-Shen Yan(颜世申), and Shi-Shou Kang(康仕寿). Chin. Phys. B, 2022, 31(7): 077503.
[8]	Synchronization in multilayer networks through different coupling mechanisms Xiang Ling(凌翔), Bo Hua(华博), Ning Guo(郭宁), Kong-Jin Zhu(朱孔金), Jia-Jia Chen(陈佳佳), Chao-Yun Wu(吴超云), and Qing-Yi Hao(郝庆一). Chin. Phys. B, 2022, 31(4): 048901.
[9]	Explosive synchronization: From synthetic to real-world networks Atiyeh Bayani, Sajad Jafari, and Hamed Azarnoush. Chin. Phys. B, 2022, 31(2): 020504.
[10]	Collective behavior of cortico-thalamic circuits: Logic gates as the thalamus and a dynamical neuronal network as the cortex Alireza Bahramian, Sajjad Shaukat Jamal, Fatemeh Parastesh, Kartikeyan Rajagopal, and Sajad Jafari. Chin. Phys. B, 2022, 31(2): 028901.
[11]	Measure synchronization in hybrid quantum-classical systems Haibo Qiu(邱海波), Yuanjie Dong(董远杰), Huangli Zhang(张黄莉), and Jing Tian(田静). Chin. Phys. B, 2022, 31(12): 120503.
[12]	Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application Yong-Bing Hu(胡永兵), Xiao-Min Yang(杨晓敏), Da-Wei Ding(丁大为), and Zong-Li Yang(杨宗立). Chin. Phys. B, 2022, 31(11): 110501.
[13]	Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay Guan Wang(王冠), Zhixia Ding(丁芝侠), Sai Li(李赛), Le Yang(杨乐), and Rui Jiao(焦睿). Chin. Phys. B, 2022, 31(10): 100201.
[14]	Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control Hongwei Zhang(张红伟), Ran Cheng(程然), and Dawei Ding(丁大为). Chin. Phys. B, 2022, 31(10): 100504.
[15]	Explosive synchronization in a mobile network in the presence of a positive feedback mechanism Dong-Jie Qian(钱冬杰). Chin. Phys. B, 2022, 31(1): 010503.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Control schemes for synchronizing two subnetworks with weak couplings

Cite this article:

Online attention