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Pinning Impulsive Synchronization of Complex Networks with Multiple Sizes of Delays via Adaptive Impulsive Intervals

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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.

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Data Availability Statement

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. 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)

    Article  Google Scholar 

  2. 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)

    MathSciNet  MATH  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. 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)

    Article  MathSciNet  Google Scholar 

  5. T. Chen, X. Liu, W. Lu, Pinning complex networks by a single controller. IEEE Trans. Circuits Syst. I Regul. Pap. 54, 1317–1326 (2007)

    Article  MathSciNet  Google Scholar 

  6. 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)

    Article  MathSciNet  Google Scholar 

  7. X. Gong, Z. Wu, Adaptive pinning impulsive synchronization of dynamical networks with time-varying delay. Adv. Differ. Equ. 240, 1–13 (2015)

    MathSciNet  MATH  Google Scholar 

  8. K. Guan, F. Tan, J. Yang, Global power synchronization of complex dynamical networks with proportional delay and impulsive effects. Neurocomputing 366, 23–34 (2019)

    Article  Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. 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)

    Article  MathSciNet  Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. L. Li, G. Mu, Synchronization of coupled complex-valued impulsive neural networks with time delays. Neural Process. Lett. 50, 2515–2527 (2019)

    Article  Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. 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)

    Article  Google Scholar 

  16. 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)

    Article  MathSciNet  Google Scholar 

  17. 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)

    Article  MathSciNet  Google Scholar 

  18. 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)

    Article  MathSciNet  Google Scholar 

  19. X. Liu, Synchronization of delayed complex-valued networks via a periodically intermittent pinning control. IEEE Int. Conf. Inf. Autom. 60, 1246–1251 (2015)

    Google Scholar 

  20. 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)

    Article  Google Scholar 

  21. 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)

    MathSciNet  MATH  Google Scholar 

  22. 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)

    Article  MathSciNet  Google Scholar 

  23. L. Papadopoulos, M.A. Porter, K.E. Daniels, D.S. Bassett, Network analysis of particles and grains. J. Complex Netw. 6, 485–565 (2018)

    Article  MathSciNet  Google Scholar 

  24. 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)

    Article  MathSciNet  Google Scholar 

  25. 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)

    Article  MathSciNet  Google Scholar 

  26. 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

    Article  Google Scholar 

  27. 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)

    MathSciNet  MATH  Google Scholar 

  28. 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)

    Article  MathSciNet  Google Scholar 

  29. 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)

    Article  MathSciNet  Google Scholar 

  30. 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)

    Article  Google Scholar 

  31. J. Wu, L. Jiao, Synchronization in complex dynamical networks with nonsymmetric coupling. Physica A 386, 513–530 (2007)

    Article  MathSciNet  Google Scholar 

  32. 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)

    Article  MathSciNet  Google Scholar 

  33. 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)

    Article  Google Scholar 

  34. Z. Wu, D. Liu, Q. Ye, Pinning impulsive synchronization of complex-variable dynamical network. Commun. Nonlinear Sci. Numer. Simul. 20, 273–280 (2015)

    Article  MathSciNet  Google Scholar 

  35. Z. Wu, G. Menichetti, C. Rahmede, G. Bianconi, Emergent complex network geometry. Sci. Rep. 5, 1–12 (2015)

    Google Scholar 

  36. W. Xia, J. Cao, Pinning synchronization of delayed dynamical networks via periodically intermittent control. Chaos 19, 1–8 (2009)

    Article  MathSciNet  Google Scholar 

  37. 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)

    MathSciNet  MATH  Google Scholar 

  38. 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)

    Article  Google Scholar 

  39. 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)

    Article  MathSciNet  Google Scholar 

  40. X. Zhang, D. Li, X. Zhang, Adaptive fuzzy impulsive synchronization of chaotic systems with random parameters. Chaos, Solitons Fract. 104, 77–83 (2017)

    Article  MathSciNet  Google Scholar 

  41. 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)

    Article  Google Scholar 

Download references

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).

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Correspondence to Zhicheng Ji.

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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

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