Volume 14, Issue 3 (Journal of Control, V.14, N.3 Fall 2020)                   JoC 2020, 14(3): 53-61 | Back to browse issues page


XML Persian Abstract Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Kazemy A. Synchronization analysis of complex dynamical networks with hybrid coupling with application to Chua’s circuit. JoC. 2020; 14 (3) :53-61
URL: http://joc.kntu.ac.ir/article-1-638-en.html
Tafresh University
Abstract:   (3480 Views)
Complex dynamic networks have been considered by researchers for their applications in modeling and analyzing many engineering issues. These networks are composed of interconnected nodes and exhibit complex behaviors that are resulted from interactions between these nodes. Synchronization, which is the concept of coordinated behavior between nodes, is the most interested behavior in these networks. This paper deals with the synchronization of complex dynamical networks with time-delays both in the states of the nodes and coupling connections between them. Moreover, constant coupling, discrete-delay coupling, and distributed-delay coupling are considered to form a hybrid coupling. Therefore, larger class and more complicated complex dynamical networks can be considered for the synchronization problem. After defining the synchronization definition, some criteria are obtained and presented in the form of linear matrix inequalities with help of the Lyapunov-Krasovskii theorem to ascertain the synchronization between each node of the network. Finally, the method is utilized for synchronization analysis of coupled Chua’s circuits which has been simulated numerically.
Full-Text [PDF 648 kb]   (567 Downloads)    
Type of Article: Research paper | Subject: Special
Received: 2019/01/12 | Accepted: 2019/04/16 | ePublished ahead of print: 2019/08/15 | Published: 2020/12/12

References
1. F. Bellamine, A. Almansoori, and A. Elkamel, "Modeling of complex dynamic systems using differential neural networks with the incorporation of a priori knowledge," Applied Mathematics and Computation, vol. 266, pp. 515-526, 2015. [DOI:10.1016/j.amc.2015.05.122]
2. A. Kazemy, "Global synchronization of neural networks with hybrid coupling: a delay interval segmentation approach," Neural Computing and Applications, vol. 30, no. 2, pp. 627-637, 2018. [DOI:10.1007/s00521-016-2661-5]
3. G. A. Pagani and M. Aiello, "The power grid as a complex network: a survey," Physica A: Statistical Mechanics and its Applications, vol. 392, no. 11, pp. 2688-2700, 2013. [DOI:10.1016/j.physa.2013.01.023]
4. H.-T. Zhang, T. Yu, J.-P. Sang, and X.-W. Zou, "Dynamic fluctuation model of complex networks with weight scaling behavior and its application to airport networks," Physica A: Statistical Mechanics and its Applications, vol. 393, pp. 590-599, 2014. [DOI:10.1016/j.physa.2013.09.005]
5. K. Liu and E. Fridman, "Networked‐based stabilization via discontinuous Lyapunov functionals," International Journal of Robust and Nonlinear Control, vol. 22, no. 4, pp. 420-436, 2012. [DOI:10.1002/rnc.1704]
6. Y. Tang, F. Qian, H. Gao, and J. Kurths, "Synchronization in complex networks and its application-a survey of recent advances and challenges," Annual Reviews in Control, vol. 38, no. 2, pp. 184-198, 2014. [DOI:10.1016/j.arcontrol.2014.09.003]
7. S. H. Strogatz, "Exploring complex networks," Nature, vol. 410, no. 6825, pp. 268-276, 2001. [DOI:10.1038/35065725]
8. Y. Zhang, D.-W. Gu, and S. Xu, "Global exponential adaptive synchronization of complex dynamical networks with neutral-type neural network nodes and stochastic disturbances," IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 10, pp. 2709-2718, 2013. [DOI:10.1109/TCSI.2013.2249151]
9. L. Zhang, Y. Wang, Y. Huang, and X. Chen, "Delay-dependent synchronization for non-diffusively coupled time-varying complex dynamical networks," Applied Mathematics and Computation, vol. 259, pp. 510-522, 2015. [DOI:10.1016/j.amc.2014.12.034]
10. L. Zhang, Y. Wang, Q. Wang, and S. Zhang, "Synchronization for Time‐Delayed Coupling Complex Dynamic Networks with Different Dimensional Nodes Via Decentralized Dynamic Compensation Controllers," Asian Journal of Control, vol. 17, no. 2, pp. 664-674, 2015. [DOI:10.1002/asjc.914]
11. A. Kazemy, "Synchronization criteria for complex dynamical networks with state and coupling time‐delays," Asian Journal of Control, vol. 19, no. 1, pp. 131-138, 2017. [DOI:10.1002/asjc.1340]
12. E. Gyurkovics, K. Kiss, and A. Kazemy, "Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control," Journal of the Franklin Institute, vol. 355, no. 17, pp. 8934-8956, 2018. [DOI:10.1016/j.jfranklin.2018.10.005]
13. L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Physical review letters, vol. 64, no. 8, p. 821, 1990. [DOI:10.1103/PhysRevLett.64.821]
14. D. Ji, J. H. Park, W. Yoo, S. Won, and S. Lee, "Synchronization criterion for Lur'e type complex dynamical networks with time-varying delay," Physics Letters A, vol. 374, no. 10, pp. 1218-1227, 2010. [DOI:10.1016/j.physleta.2010.01.005]
15. B. Wang and Z.-H. Guan, "Chaos synchronization in general complex dynamical networks with coupling delays," Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1925-1932, 2010. [DOI:10.1016/j.nonrwa.2009.04.020]
16. W. Yu, G. Chen, and M. Cao, "Consensus in directed networks of agents with nonlinear dynamics," IEEE Transactions on Automatic Control, vol. 56, no. 6, pp. 1436-1441, 2011. [DOI:10.1109/TAC.2011.2112477]
17. T. H. Lee, D. Ji, J. H. Park, and H. Y. Jung, "Decentralized guaranteed cost dynamic control for synchronization of a complex dynamical network with randomly switching topology," Applied Mathematics and Computation, vol. 219, no. 3, pp. 996-1010, 2012. [DOI:10.1016/j.amc.2012.07.004]
18. M. Fang, "Synchronization for complex dynamical networks with time delay and discrete-time information," Applied Mathematics and Computation, vol. 258, pp. 1-11, 2015. [DOI:10.1016/j.amc.2015.01.106]
19. L. Yi‐ping and Z. Bi‐feng, "Guaranteed Cost Synchronization of Complex Network Systems with Delay," Asian Journal of Control, vol. 17, no. 4, pp. 1274-1284, 2015. [DOI:10.1002/asjc.992]
20. X. Yang, J. Cao, and J. Lu, "Synchronization of randomly coupled neural networks with Markovian jumping and time-delay," IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 2, pp. 363-376, 2013. [DOI:10.1109/TCSI.2012.2215804]
21. H. Zhang, D. Gong, B. Chen, and Z. Liu, "Synchronization for coupled neural networks with interval delay: a novel augmented Lyapunov-Krasovskii functional method," IEEE Transactions on Neural Networks and Learning Systems,, vol. 24, no. 1, pp. 58-70, 2013. [DOI:10.1109/TNNLS.2012.2225444]
22. C. Zheng and J. Cao, "Robust synchronization of coupled neural networks with mixed delays and uncertain parameters by intermittent pinning control," Neurocomputing, vol. 141, pp. 153-159, 2014. [DOI:10.1016/j.neucom.2014.03.042]
23. B. Huang, H. Zhang, D. Gong, and J. Wang, "Synchronization analysis for static neural networks with hybrid couplings and time delays," Neurocomputing, vol. 148, pp. 288-293, 2015. [DOI:10.1016/j.neucom.2013.11.053]
24. M. Kalpana, P. Balasubramaniam, and K. Ratnavelu, "Direct delay decomposition approach to synchronization of chaotic fuzzy cellular neural networks with discrete, unbounded distributed delays and Markovian jumping parameters," Applied Mathematics and Computation, vol. 254, pp. 291-304, 2015. [DOI:10.1016/j.amc.2014.12.133]
25. K. Gu, J. Chen, and V. L. Kharitonov, Stability of time-delay systems. Springer Science & Business Media, 2003. [DOI:10.1007/978-1-4612-0039-0]
26. W.-H. Chen, Z. Jiang, X. Lu, and S. Luo, "H∞ synchronization for complex dynamical networks with coupling delays using distributed impulsive control," Nonlinear Analysis: Hybrid Systems, vol. 17, pp. 111-127, 2015.
27. Z. Tang, J. Feng, and Y. Zhao, "Global synchronization of nonlinear coupled complex dynamical networks with information exchanges at discrete-time," Neurocomputing, vol. 151, pp. 1486-1494, 2015. [DOI:10.1016/j.neucom.2014.10.037]
28. Y. Xu, W. Zhou, J. a. Fang, C. Xie, and D. Tong, "Finite-time synchronization of the complex dynamical network with non-derivative and derivative coupling," Neurocomputing, vol. 173, pp. 1356-1361, 2016. [DOI:10.1016/j.neucom.2015.09.008]
29. A. Kazemy and J. Cao, "Consecutive synchronization of a delayed complex dynamical network via distributed adaptive control approach," International Journal of Control, Automation and Systems, vol. 16, no. 6, pp. 2656-2664, 2018. [DOI:10.1007/s12555-017-0718-6]
30. A. Kazemy and É. Gyurkovics, "Sliding mode synchronization of a delayed complex dynamical network in the presence of uncertainties and external disturbances," Transactions of the Institute of Measurement and Control, p. 0142331218805533, 2018. [DOI:10.1177/0142331218805533]
31. A. Kazemy and K. Shojaei, "Synchronization of Complex Dynamical Networks with Dynamical Behavior Links," Asian Journal of Control, 2020.
32. Y. Liu, Z. Wang, J. Liang, and X. Liu, "Synchronization and state estimation for discrete-time complex networks with distributed delays," IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 38, no. 5, pp. 1314-1325, 2008. [DOI:10.1109/TSMCB.2008.925745]
33. R. A. Horn, R. A. Horn, and C. R. Johnson, Matrix analysis. Cambridge university press, 1990.
34. W.-H. Chen, D. Wei, and X. Lu, "Global exponential synchronization of nonlinear time-delay Lur'e systems via delayed impulsive control," Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 3298-3312, 2014. [DOI:10.1016/j.cnsns.2014.01.018]
35. A. Kazemy and M. Farrokhi, "Synchronization of chaotic Lur'e systems with state and transmission line time delay: a linear matrix inequality approach," Transactions of the Institute of Measurement and Control, vol. 39, no. 11, pp. 1703-1709, 2017. [DOI:10.1177/0142331216644497]

Add your comments about this article : Your username or Email:
CAPTCHA

Send email to the article author


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

© 2021 CC BY-NC 4.0 | Journal of Control

Designed & Developed by : Yektaweb