Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems

doi:10.1088/1674-1056/21/3/030505

Abstract We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory, the fractional order differential inequality, and the adaptive strategy. This synchronization approach is simple, universal, and theoretically rigorous. It enables the synchronization of0 fractional-order chaotic systems to be achieved in a systematic way. The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.

Keywords: synchronization modified adaptive controller incommensurate fractional-order chaotic system

Received: 02 August 2011
Revised: 17 October 2011
Accepted manuscript online:

PACS:

05.45.Xt

(Synchronization; coupled oscillators)

Fund: Project supported by the Natural Science Foundation of Hebei Province, China (Grant No. A2010000343).

Corresponding Authors: Yang Shi-Ping,yangship@mail.hebtu.edu.cn
E-mail: yangship@mail.hebtu.edu.cn

Cite this article:

Zhang Ruo-Xun(张若洵) and Yang Shi-Ping(杨世平) Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems 2012 Chin. Phys. B 21 030505

[1]	Bagley R L and Calico R A 1991 J. Guid. Control Dyn. 14 304
[2]	Sun H H, Abdelwahad A A and Onaral B1984 Autom. Control 29 441
[3]	Ichise M, Nagayanagi Y and Kojima T 1971 J. Electroanal. Chem. Interfacial Electrochem. 33 253
[4]	Heaviside O 1971 Electromagnetic Theory (New York: Chelsea)
[5]	Hartley T T, Lorenzo C F and Qammer H K 1995 IEEE Trans. CAS I 42 485
[6]	Grigorenko I and Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[7]	Xu Z and Liu C X 2008 Chin. Phys. B 17 4033
[8]	Li C G and Chen G R 2004 Solitons & Fractals 22 549
[9]	Deng W H and Li C P 2005 Physica A 353 61
[10]	Zhang R X and Yang S P 2009 Acta Phys. Sin. 58 2957 (in Chinese)
[11]	Qi G Y, Chen G R, Du S Z and Chen Z Q 2005 Physica A 352 295
[12]	Li C P and Deng W H 2006 Int. J. Modern Phys. B 20 791
[13]	Lu J G 2006 Physica A 359 107
[14]	Wu X J, Lu H T and Shen S L 2009 Phys. Lett. A 373 2329
[15]	Zhang R X and Yang S P 2010 Chin. Phys. B 19 020510
[16]	Odibat Z M 2010 Nonlinear Dyn. 60 479
[17]	Wang X Y, Zhang Y L, Lin D and Zhang N 2011 Chin. Phys. B 20 030506
[18]	Tavazoei M S and Haeri M 2008 Physica A 387 57
[19]	Zhang R X and Yang S P 2011 Nonlinear Dyn. 66 831
[20]	Lu J G 2006 Chaos Solition. Fract. 27 519
[21]	Wu C J, Zhang Y B and Yang N N 2011 Chin. Phys. B 20 060505
[22]	Wang M J, Wang X Y and Niu Y J 2011 Chin. Phys. B 20 010508
[23]	Qi D L, Yang J and Zhang J L 2010 Chin. Phys. B 19 100506
[24]	Zhang R X and Yang S P 2011 Chin. Phys. B 20 090512
[25]	Niu Y J, Wang X Y, Nian F Z and Wang M J 2010 Chin. Phys. B 19 120507.
[26]	Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
[27]	Li Y, Chen Y Q and Podlubny I 2010 Computers & Mathematics with Applications 59 1810
[28]	Gorenflo R and Mainardi F 1997 Fractals and Fractional Calculus (New York: Springer)
[29]	Tavazoei M S and Haeri M 2008 Physica D 237 2628
[30]	Popov V M 1973 Hyperstability of Control Systems (Berlin: Springer-Verlag)
[31]	Deng W H 2007 J. Comput. Phys. 227 1510
[32]	Song L J, Yang Y and Xu S Y 2010 Nonlinear Analysis: Theory Methods & Applications 72 2326
[33]	Dadras S, Momeni H, Qi G Y and Wang Z L 2011 Nonlinear Dyn. 67 1161

[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 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.
[14]	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.
[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

Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems

Cite this article:

Online attention