Abstract
The leader-following issue for a class of nonlinearly coupled complex networks with multiple time-varying delays was investigated in this study. A distributed controller was introduced for realizing the exponential synchronization of the complex network with different delay scales that are known in advance. The Lyapunov stability theorem and mathematical induction method were used to obtain delay-dependent criteria for global impulsive synchronization. Additionally, an adaptive strategy was adopted to establish appropriate impulsive intervals suitable for various delays. The fact that the proposed adaptive scheme is more general and less conservative enables the effective release of the constriction caused by unknown delay scales. Furthermore, the pinning impulsive control method enables the control cost to be further reduced. Finally, several numerical simulations were performed to evaluate the effectiveness of the mathematical deductions.
Similar content being viewed by others
Data Availability Statement
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
References
L.P. Andrade, R.P. Espindola, G.C. Pereira, N.F.F. Ebecken, Exploring complex networks in the plankton. IEEE Lat. Am. Trans. 14, 3838–3846 (2016)
A. Bandyopadhyay, S. Kar, Coevolution of cooperation and network structure in social dilemmas in evolutionary dynamic complex network. Appl. Math. Comput. 320, 710–730 (2018)
S. Cai, X. Li, Q. Jia, Z. Liu, Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach. Nonlinear Dyn. 85, 2405–2423 (2016)
J. Chen, J. Li, R. Zhang, C. Wei, Distributed fuzzy consensus of uncertain topology structure multi-agent systems with non-identical partially unknown control directions. Appl. Math. Comput. 362, 124581 (2019)
T. Chen, X. Liu, W. Lu, Pinning complex networks by a single controller. IEEE Trans. Circuits Syst. I Regul. Pap. 54, 1317–1326 (2007)
T. Chen, S. Peng, Z. Zhang, Finite-time synchronization of Markovian jumping complex networks with non-identical nodes and impulsive effects. Entropy 21, 779 (2019)
X. Gong, Z. Wu, Adaptive pinning impulsive synchronization of dynamical networks with time-varying delay. Adv. Differ. Equ. 240, 1–13 (2015)
K. Guan, F. Tan, J. Yang, Global power synchronization of complex dynamical networks with proportional delay and impulsive effects. Neurocomputing 366, 23–34 (2019)
Y. Guan, Y. Wu, H. Wu, Y. Li, S. He, Synchronization of complex dynamical networks with actuator saturation by using sampled-data control. Circuits Syst. Signal Process. 38, 5508–5527 (2019)
W. He, X. Gao, W. Zhong, F. Qian, Secure impulsive synchronization control of multi-agent systems under deception attacks. Inf. Sci. (NY) 459, 354–368 (2018)
Y. Kan, J. Lu, J. Qiu, J. Kurths, Exponential synchronization of time-varying delayed complex-valued neural networks under hybrid impulsive controllers. Neural Netw. 114, 157–163 (2019)
L. Li, G. Mu, Synchronization of coupled complex-valued impulsive neural networks with time delays. Neural Process. Lett. 50, 2515–2527 (2019)
L. Li, X. Shi, J. Liang, Synchronization of impulsive coupled complex-valued neural networks with delay: the matrix measure method. Neural Netw. 117, 285–294 (2019)
M. Li, X. Li, X. Han, J. Qiu, Leader-following synchronization of coupled time-delay neural networks via delayed impulsive control. Neurocomputing 357, 101–107 (2019)
S. Li, X. Peng, Y. Tang, Y. Shi, Finite-time synchronization of time-delayed neural networks with unknown parameters via adaptive control. Neurocomputing 308, 65–74 (2018)
T. Li, T. Wang, X. Yang, S. Fei, Pinning cluster synchronization for delayed dynamical networks via Kronecker product. Circuits Syst. Signal Process. 32, 1907–1929 (2013)
G. Liu, J.H. Park, S. Xu, G. Zhuang, Robust non-fragile \(H_\infty \) fault detection filter design for delayed singular Markovian jump systems with linear fractional parametric uncertainties. Nonlinear Anal. Hybrid Syst. 32, 65–78 (2019)
G. Liu, S. Xu, J.H. Park, G. Zhuang, Reliable exponential \(H_\infty \) filtering for singular Markovian jump systems with time-varying delays and sensor failures. Int. J. Robust Nonlinear Control. 28, 4230–4245 (2018)
X. Liu, Synchronization of delayed complex-valued networks via a periodically intermittent pinning control. IEEE Int. Conf. Inf. Autom. 60, 1246–1251 (2015)
Y. Long, J.H. Park, D. Ye, Transmission-dependent fault detection and isolation strategy for networked systems under finite capacity channels. IEEE Trans. Cybern. 47, 2266–2278 (2017)
J. Lu, X. Guo, T. Huang, Z. Wang, Consensus of signed networked multi-agent systems with nonlinear coupling and communication delays. Appl. Math. Comput. 350, 153–162 (2019)
D. Ning, X. Wu, H. Feng, Y. Chen, J. Lu, Inter-layer generalized synchronization of two-layer impulsively-coupled networks. Commun. Nonlinear Sci. Numer. Simul. 79, 104947 (2019)
L. Papadopoulos, M.A. Porter, K.E. Daniels, D.S. Bassett, Network analysis of particles and grains. J. Complex Netw. 6, 485–565 (2018)
Y. Pei, M. Bohner, D. Pi, Impulsive synchronization of time-scales complex networks with time-varying topology. Commun. Nonlinear Sci. Numer. Simul. 80, 104981 (2020)
Z. Tang, J.H. Park, Y. Wang, J. Feng, Impulsive synchronization of derivative coupled neural networks with cluster-tree topology. IEEE Trans. Netw. Sci. Eng. 7, 1788–1798 (2020)
Z. Tang, J.H. Park, Y. Wang, W.X. Zheng, Synchronization on Lur’e cluster networks with proportional delay: impulsive effects method. IEEE Trans. Syst. Man, Cybern. Syst. (2019). https://doi.org/10.1109/tsmc.2019.2943933
J. Wang, Synchronization of complex networks with random coupling strengths and mixed probabilistic time-varying coupling delays using sampled data. Abstr. Appl. Anal. 2014, 845304 (2014)
X. Wang, X. Liu, K. She, S. Zhong, Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes. Nonlinear Anal. Hybrid Syst. 26, 307–318 (2017)
X. Wang, K. She, S. Zhong, J. Cheng, Synchronization of complex networks with non-delayed and delayed couplings via adaptive feedback and impulsive pinning control. Nonlinear Dyn. 86, 165–176 (2016)
Y. Wang, D. Tong, Q. Chen, W. Zhou, Exponential synchronization of chaotic systems with stochastic perturbations via quantized feedback control. Circuits, Syst. Signal Process. 39, 474–491 (2020)
J. Wu, L. Jiao, Synchronization in complex dynamical networks with nonsymmetric coupling. Physica A 386, 513–530 (2007)
K. Wu, B. Li, Y. Du, S. Du, Synchronization for impulsive hybrid-coupled reaction-diffusion neural networks with time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 82, 105031 (2020)
Y. Wu, Y. Li, W. Li, Synchronization of random coupling delayed complex networks with random and adaptive coupling strength. Nonlinear Dyn. 96, 2393–2412 (2019)
Z. Wu, D. Liu, Q. Ye, Pinning impulsive synchronization of complex-variable dynamical network. Commun. Nonlinear Sci. Numer. Simul. 20, 273–280 (2015)
Z. Wu, G. Menichetti, C. Rahmede, G. Bianconi, Emergent complex network geometry. Sci. Rep. 5, 1–12 (2015)
W. Xia, J. Cao, Pinning synchronization of delayed dynamical networks via periodically intermittent control. Chaos 19, 1–8 (2009)
Q. Xu, X. Xu, S. Zhuang, J. Xiao, C. Song, C. Che, New complex projective synchronization strategies for drive-response networks with fractional complex-variable dynamics. Appl. Math. Comput. 338, 552–566 (2018)
C. Yi, C. Xu, J. Feng, J. Wang, Y. Zhao, Pinning synchronization for reaction-diffusion neural networks with delays by mixed impulsive control. Neurocomputing 339, 270–278 (2019)
J. Yogambigai, M.S. Ali, H. Alsulami, M.S. Alhodaly, Impulsive and pinning control synchronization of Markovian jumping complex dynamical networks with hybrid coupling and additive interval time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 85, 105215 (2020)
X. Zhang, D. Li, X. Zhang, Adaptive fuzzy impulsive synchronization of chaotic systems with random parameters. Chaos, Solitons Fract. 104, 77–83 (2017)
P. Zhou, S. Cai, J. Shen, Z. Liu, Adaptive exponential cluster synchronization in colored community networks via a periodically intermittent pinning control. Nonlinear Dyn. 92, 905–921 (2018)
Acknowledgements
This work was supported by the National Key R & D Program of China (Grant No. 2018YFB1701903), the National Natural Science Foundation of China (Grant No. 61803180, No. 61973138), the China Postdoctoral Science Foundation (Grant No. 2020M681484), and the Natural Science Foundation of Jiangsu Province (Grant No. BK20180599).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ding, D., Tang, Z., Wang, Y. et al. Pinning Impulsive Synchronization of Complex Networks with Multiple Sizes of Delays via Adaptive Impulsive Intervals. Circuits Syst Signal Process 40, 4259–4278 (2021). https://doi.org/10.1007/s00034-021-01682-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-021-01682-0