Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(6): 060510    DOI: 10.1088/1674-1056/22/6/060510
GENERAL Prev   Next  

A novel study for impulsive synchronization of fractional-order chaotic systems

Liu Jin-Gui (刘金桂)
Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, China
Abstract  The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. The synchronization criterion is suitable for the case of the order 0 < q ≤ 1. It is more general than those of the known results. Simulation results are given to show the effectiveness of the proposed synchronization criterion.
Keywords:  fractional-order      chaotic systems      impulsive synchronization      Gronwall-Bellman's inequality  
Received:  04 October 2012      Revised:  08 December 2012      Accepted manuscript online: 
PACS:  05.45.Gg (Control of chaos, applications of chaos)  
  05.45.Xt (Synchronization; coupled oscillators)  
Fund: Project supported by Scientific Research Foundation of Huaiyin Institute of Technology (Grant No. HGA1102).
Corresponding Authors:  Liu Jin-Gui     E-mail:  liujg2004@126.com

Cite this article: 

Liu Jin-Gui (刘金桂) A novel study for impulsive synchronization of fractional-order chaotic systems 2013 Chin. Phys. B 22 060510

[1] Diethelm K and Ford N J 2002 J. Math. Anal. Appl. 265 229
[2] Deng W H 2010 Nonlinear Anal.: TMA 272 1768
[3] Lu J G and Chen G R 2006 Chaos, Solitons and Fractals 27 685
[4] Li C P and Peng G J 2004 Chaos, Solitons and Fractals 22 443
[5] Lu J G 2006 Phys. Lett. A 354 305
[6] Zhang W W, Zhou S B, Li H and Zhu H 2009 Chaos, Solitons and Fractals 42 1684
[7] Park J H 2009 Mod. Phys. Lett. B 23 1889
[8] Chen D L, Sun J T and Huang C S 2006 Chaos, Solitons and Fractals 28 213
[9] Li G H, Zhou S P and Yang K 2006 Phys. Lett. A 355 326
[10] Zhang Q J and Lu J A 2008 Phys. Lett. A 372 1416
[11] Chen Y, Chen X X and Gu S S 2007 Nonlinear Anal. 66 1929
[12] Li G H 2009 Chaos, Solitons and Fractals 41 2630
[13] Wang S G and Yao H X 2011 Chin. Phys. B 20 090513
[14] Haeri M and Dehghani M 2006 Phys. Lett. A 356 226
[15] Liu X Z 2009 Nonlinear Anal. 71 1320
[16] Wang X Y, Zhang Y L, Lin D and Zhang N 2011 Chin. Phys. B 20 030506
[17] Zhong Q S, Bao J F, Yu Y B and Liao X F 2008 Chin. Phys. Lett. 25 2812
[18] Ma T D, Jiang W B and Fu J 2012 Acta Phys. Sin. 61 090503 (in Chinese)
[19] Fu J, Yu M and Ma T D 2011 Chin. Phys. B 20 120508
[20] Hu T C, Qian D L and Li C P 2009 Comm. Appl. Math. Comput. 23 97
[21] Plaat O 1971 Ordinary Differential Equations (San Francisco: Holden-Day) pp. 275-279
[22] Lakshmikantham V, Bainov D D and Simeonov P S 1989 Theory of Impulsive Differential Equations (Singapore: World Scientific) pp. 105-108
[23] Deng W H 2007 J. Comput. Phys. 227 1510
[1] Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse
Zhi-Jun Li(李志军), Wen-Qiang Xie(谢文强), Jin-Fang Zeng(曾金芳), and Yi-Cheng Zeng(曾以成). Chin. Phys. B, 2023, 32(1): 010503.
[2] A mathematical analysis: From memristor to fracmemristor
Wu-Yang Zhu(朱伍洋), Yi-Fei Pu(蒲亦非), Bo Liu(刘博), Bo Yu(余波), and Ji-Liu Zhou(周激流). Chin. Phys. B, 2022, 31(6): 060204.
[3] The dynamics of a memristor-based Rulkov neuron with fractional-order difference
Yan-Mei Lu(卢艳梅), Chun-Hua Wang(王春华), Quan-Li Deng(邓全利), and Cong Xu(徐聪). Chin. Phys. B, 2022, 31(6): 060502.
[4] Solutions and memory effect of fractional-order chaotic system: A review
Shaobo He(贺少波), Huihai Wang(王会海), and Kehui Sun(孙克辉). Chin. Phys. B, 2022, 31(6): 060501.
[5] Explosive synchronization: From synthetic to real-world networks
Atiyeh Bayani, Sajad Jafari, and Hamed Azarnoush. Chin. Phys. B, 2022, 31(2): 020504.
[6] 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.
[7] 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.
[8] Complex network perspective on modelling chaotic systems via machine learning
Tong-Feng Weng(翁同峰), Xin-Xin Cao(曹欣欣), and Hui-Jie Yang(杨会杰). Chin. Phys. B, 2021, 30(6): 060506.
[9] Dynamical analysis, circuit realization, and application in pseudorandom number generators of a fractional-order laser chaotic system
Chenguang Ma(马晨光), Santo Banerjee, Li Xiong(熊丽), Tianming Liu(刘天明), Xintong Han(韩昕彤), and Jun Mou(牟俊). Chin. Phys. B, 2021, 30(12): 120504.
[10] Adaptive synchronization of chaotic systems with less measurement and actuation
Shun-Jie Li(李顺杰), Ya-Wen Wu(吴雅文), and Gang Zheng(郑刚). Chin. Phys. B, 2021, 30(10): 100503.
[11] Finite-time Mittag-Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions
Chong Chen(陈冲), Zhixia Ding(丁芝侠), Sai Li(李赛), Liheng Wang(王利恒). Chin. Phys. B, 2020, 29(4): 040202.
[12] Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks
Yu-Jiao Huang(黄玉娇), Xiao-Yan Yuan(袁孝焰), Xu-Hua Yang(杨旭华), Hai-Xia Long(龙海霞), Jie Xiao(肖杰). Chin. Phys. B, 2020, 29(2): 020703.
[13] Coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions
Yu-Jiao Huang(黄玉娇), Shi-Jun Chen(陈时俊), Xu-Hua Yang(杨旭华), Jie Xiao(肖杰). Chin. Phys. B, 2019, 28(4): 040701.
[14] Primary resonance of fractional-order Duffing-van der Pol oscillator by harmonic balance method
Sujuan Li(李素娟), Jiangchuan Niu(牛江川), Xianghong Li(李向红). Chin. Phys. B, 2018, 27(12): 120502.
[15] Ghost images reconstructed from fractional-order moments with thermal light
De-Zhong Cao(曹德忠), Qing-Chen Li(李清晨), Xu-Cai Zhuang(庄绪财), Cheng Ren(任承), Su-Heng Zhang(张素恒), Xin-Bing Song(宋新兵). Chin. Phys. B, 2018, 27(12): 123401.
No Suggested Reading articles found!