JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (11): 53-60.doi: 10.6040/j.issn.1671-9352.0.2022.322

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Topology identification of fractional complex networks based on variable substitution control method

Weiyuan MA1(),Zhiming LI2,Changping DAI1   

  1. 1. School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
    2. Guizhou Aerospace Tianma Electromechanical Technology Co., Ltd., Zunyi 563000, Guizhou, China
  • Received:2022-05-30 Online:2023-11-20 Published:2023-11-07

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Abstract:

In this paper, synchronization and topology identification of fractional-order complex dynamical networks based on the variable substitution control method are studied. The considered network constructs a response network and parameter update law with variable substitution control. Based on the stability theory of fractional differential systems, the criteria for realizing topology identification and synchronization are deduced. Finally, the effectiveness and feasibility of the proposed method are verified by numerical simulation.

Key words: variable substitution control, topology identification, synchronization, complex network

CLC Number: 

  • N941.4

Fig.1

The evolution effect of the unknown topology over time in Example 1"

Fig.2

Synchronization error in Example 1"

Fig.3

The overall mean error for different fractional orders in Example 1"

Fig.4

The identification effect of unknown topologies in Example 2"

Fig.5

The synchronization error in Example 2"

Fig.6

The overall mean error for different fractional orders in Example 2"

1 LIU Guoping , KADIRKAMANATHAN V , BILLINGS S A . Variable neural networks for adaptive control of nonlinear systems[J]. IEEE Transactions on Systems, Man, and Cybernetics: Part C, 1999, 29 (1): 34- 43.
doi: 10.1109/5326.740668
2 MA Weiyuan , LI Zhiming , MA Nuri . Synchronization of discrete fractional-order complex networks with and without unknown topology[J]. Chaos, 2022, 32, 013112.
doi: 10.1063/5.0072207
3 GUI Zhifang , WU Xiaofeng , CHEN Yun . Global synchronization of multi-scroll saturated chaotic systems via single-state linear feedback control[J]. International Journal of Modern Physics B, 2013, 27 (5): 1350007.
doi: 10.1142/S0217979213500070
4 SUN Jitao , ZHANG Yinping . Impulsive control of n-scroll grid attractors[J]. International Journal of Bifurcation and Chaos, 2004, 14 (9): 3295- 3301.
doi: 10.1142/S0218127404011326
5 WU Yongbao , ZHU Jilin , LI Wenxue . Intermittent discrete observation control for synchronization of stochastic neural networks[J]. IEEE Transactions on Cybernetics, 2019, 50 (6): 2414- 2424.
6 SU Haipeng , LUO Runzi , HUANG Meichun , et al. Practical fixed time active control scheme for synchronization of a class of chaotic neural systems with external disturbances[J]. Chaos, Solitons & Fractals, 2022, 157, 111917.
7 王震, 吴云天, 邹永杰. 多涡卷Jerk电路混沌系统的分析与滑模控制[J]. 西安科技大学学报, 2009, 29 (6): 765- 768.
doi: 10.3969/j.issn.1672-9315.2009.06.024
WANG Zhen , WU Yuntian , ZOU Yongjie . Analysis and sliding mode control of multi-scroll Jerk circuit chaotic system[J]. Journal of Xi'an University of Science and Technology, 2009, 29 (6): 765- 768.
doi: 10.3969/j.issn.1672-9315.2009.06.024
8 PECORA L M , CARROLL T L . Synchronization in chaotic systems[J]. Physical Review Letters, 1990, 64 (8): 821- 824.
doi: 10.1103/PhysRevLett.64.821
9 SI Gangquan , SUN Zhiyong , ZHANG Hongying , et al. Parameter estimation and topology identification of uncertain fractional order complex networks[J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17 (12): 5158- 5171.
doi: 10.1016/j.cnsns.2012.05.005
10 CHEN Yun , WU Xiaofeng , LIU Zhong . Global chaos synchronization of electro-mechanical gyrostat systems via variable substitution control[J]. Chaos Soliton Fractals, 2009, 42 (2): 1197- 1205.
doi: 10.1016/j.chaos.2009.03.014
11 ZHONG G Q , TANG WALLACE K S . Circuitry implementation and synchronization of Chen's attractor[J]. International Journal of Bifurcation and Chaos, 2002, 12 (6): 1423- 1427.
doi: 10.1142/S0218127402005224
12 LIU Zhong, CHEN Yun, WU Xiaofeng. Global chaos synchronization of the brushless DC motor systems via variable substitution control[C]// Proceedings of 2009 International Workshop on Chaos-Fractals Theories and Applications. Shenyang: IEEE, 2009: 44-47.
13 CHEN Yun , WU Xiaofeng . Global chaos synchronization of nonautonomous systems via variable substitution control[J]. International Journal of Bifurcation and Chaos, 2008, 18 (12): 3719- 3730.
doi: 10.1142/S0218127408022676
14 LU Junan , WU Xiaoqun , LV Jinhu . Synchronization of a unified chaotic system and the application in secure communication[J]. Physical Review A, 2002, 305 (6): 365- 370.
15 AGIZA H N . Chaos synchronization of Lü dynamical system[J]. Nonlinear Analysis, 2004, 58 (1/2): 11- 20.
16 WU Xiaofeng , ZHAO Yi , HUANG Xiaohua . Some new criteria for lag synchronization of chaotic Lur'e systems by replacing variables control[J]. Journal of Control Theory and Applications, 2004, 2 (3): 259- 266.
doi: 10.1007/s11768-004-0007-9
17 ELABBASY E M , AGIZA H N , ELDESSOKY M M . Synchronization of modified Chen system[J]. International Journal of Bifurcation and Chaos, 2004, 14 (11): 3969- 3979.
doi: 10.1142/S0218127404011740
18 WU Xiaoqun , LI Yanan , WEI Juan , et al. Inter-layer synchronization in two-layer networks via variable substitution control[J]. Journal of the Franklin Institute, 2020, 357 (4): 2371- 2387.
doi: 10.1016/j.jfranklin.2019.12.019
19 LI Changping , DENG Weihua . Remarks on fractional derivatives[J]. Applied Mathematics and Computation, 2007, 187 (2): 777- 784.
doi: 10.1016/j.amc.2006.08.163
20 LI Zhiming , MA Weiyuan , MA Nuri . Partial topology identification of tempered fractional-order complex networks via synchronization method[J]. Mathematical Methods in the Applied Sciences, 2023, 46 (3): 3066- 3079.
doi: 10.1002/mma.7549
21 LI Yan , CHEN Yangquan , PODLUBNY I . MittagLeffler stability of fractional order nonlinear dynamic systems[J]. Automatica, 2009, 45 (8): 1965- 1969.
doi: 10.1016/j.automatica.2009.04.003
22 AGUILA-CAMACHO N , DUARTE-MERMOUD M A , GALLEGO J A . Lyapunov functions for fractional order systems[J]. Communications in Nonlinear Science and Numerical Simulation, 2014, 19 (9): 2951- 2957.
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