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Finite-time synchronization of complex delayed networks via intermittent control with multiple switched periods

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Abstract

In this paper, an intermittent control approach with multiple switched periods is proposed for the finite-time synchronization in complex networks with non-delay and time-varying delay couplings. Based on finite-time stability theory, the theory of Kronecker product of matrices and the inequality techniques, some novel delay-dependent criteria are obtained to ensure finite-time synchronization for the complex networks, which avoid complex computation on the matrix inequalities. Moreover, the convergence time does not depend on control widths and control periods for the proposed intermittent controller with multiple switched periods. When the control width index \(\theta \rightarrow 1^-\), the finite-time impulsive synchronization control schemes as special cases are also given. Especially, the traditional synchronization criteria for some models are improved in the convergence time by using the novel periodical intermittent feedback control and the finite-time impulsive control. The results here are also applicable to both directed and undirected weighted networks without any other conditions. Finally, one numerical example with chaotic nodes is given to demonstrate the effectiveness of the proposed controllers.

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References

  1. Newman, M.: The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Qin, H., Ma, J., Jin, W., Wang, C.: Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci. China Technol. Sci. 57, 936–946 (2014)

    Article  Google Scholar 

  3. Song, X., Wang, C., Ma, J., Tang, J.: Transition of electric activity of neurons induced by chemical and electric autapses. Sci. China Technol. Sci. 58, 1007–1014 (2015)

    Article  Google Scholar 

  4. Lee, T., Park, J., Ji, D., Kwon, O., Lee, S.: Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control. Appl. Math. Comput. 218, 6469–6481 (2012)

    MathSciNet  MATH  Google Scholar 

  5. Xu, D., Su, Z.: Synchronization criterions and pinning control of general complex networks with time delay. Appl. Math. Comput. 215, 1593–1608 (2009)

    MathSciNet  MATH  Google Scholar 

  6. Liang, Y., Wang, X., Eustace, J.: Adaptive synchronization in complex networks with non-delay and variable delay couplings via pinning control. Neurocomputing 123, 292–298 (2014)

    Article  Google Scholar 

  7. Song, Q.: Synchronization analysis of coupled connected neural networks with mixed time delays. Neurocomputing 72, 3907–3914 (2009)

    Article  Google Scholar 

  8. Yu, W., Chen, G., Lü, J., Kurths, J.: Synchronization via pinning control on general complex networks. J. SIAM J. Control Optim. 51, 1395–1416 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang, G., Cao, J., Lu, J.: Outer synchronization between two nonidentical networks with circumstance noise. Phys. A 389, 1480–1488 (2010)

    Article  Google Scholar 

  10. Hu, C., Mei, X., Yu, J., Jiang, H.: Finite-time uniform stability of functional differential equations with applications in network synchronization control. Chaos Solitons Fractal. 62, 10–22 (2014)

    Article  MathSciNet  Google Scholar 

  11. Zhao, M., Zhang, H., Wang, Z., Liang, H.: Synchronization between two general complex networks with time-delay by adaptive periodically intermittent pinning control. Neurocomputing 144, 215–221 (2014)

    Article  Google Scholar 

  12. Zhao, M., Zhang, H., Wang, Z., Liang, H.: Observer-based lag synchronization between two different complex networks. Commun. Nonlinear Sci. Numer. Simul. 19, 2048–2059 (2014)

    Article  MathSciNet  Google Scholar 

  13. Cai, S., Zhou, J., Xiang, L., Liu, Z.: Robust impulsive synchronization of complex delayed dynamical networks. Phys. Lett. A 372, 4990–4995 (2008)

    Article  MATH  Google Scholar 

  14. Zhou, J., Xiang, L., Liu, Z.: Synchronization in complex delayed dynamical networks with impulsive effects. Phys. A 384, 684–692 (2007)

    Article  MathSciNet  Google Scholar 

  15. Zheng, S., Dong, G., Bi, Q.: Impulsive synchronization of complex networks with non-delayed and delayed coupling. Phys. Lett. A 373, 4255–4259 (2009)

    Article  MATH  Google Scholar 

  16. Cao, J., Lu, J.: Adaptive synchronization of neural networks with or without time-varying delay. Chaos 16, 013133 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhang, Q., Lu, J., Lü, J., Tse, C.: Adaptive feedback synchronization of a general complex dynamical network with delayed nodes. IEEE Trans. Circuits Syst. II Exp. Briefs 55, 183–187 (2008)

    Article  Google Scholar 

  18. Wang, B., Guan, Z.: Chaos synchronization in general complex dynamical networks with coupling delays. Nonlinear Anal. Real. 11, 1925–1932 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wu, H., Li, R., Zhang, X., Yao, R.: Adaptive finite-time complete periodic synchronization of memristive neural networks with time delays. Neural Process. Lett. 42, 563–583 (2015)

    Article  Google Scholar 

  20. Aghababa, M., Khanmohammadi, S., Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl. Math. Model 35, 3080–3091 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Boulkroune, A., Bouzeriba, A., Hamel, S., Bouden, T.: A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems. Nonlinear Dyn. 78(1), 433–447 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Boulkroune, A., Bouzeriba, A., Hamel, S., Bouden, T.: Adaptive fuzzy control-based projective synchronization of uncertain nonaffine chaotic systems. Complexity 21(2), 180–192 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. Boulkroune, A., M’saad, M.: Fuzzy adaptive observer-based projective synchronization for nonlinear systems with input nonlinearity. J. Vib. Control 18, 437–450 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sun, H., Li, N., Zhao, D., Zhang, Q.: Synchronization of complex networks with coupling delays via adaptive pinning intermittent control. Int. J. Autom. Comput. 10, 312–318 (2013)

    Article  Google Scholar 

  25. Li, C., Feng, G., Liao, X.: Stabilization of nonlinear systems via periodically intermittent control. IEEE Trans. Circuits Syst. II Exp. Briefs 54, 1019–1023 (2007)

    Article  Google Scholar 

  26. Li, C., Liao, X., Huang, T.: Exponential stabilization of chaotic systems with delay by periodically intermittent control. Chaos 17, 013103 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  27. Zochowski, M.: Intermittent dynamical control. Phys. D 145, 181–190 (2000)

    Article  MATH  Google Scholar 

  28. Yang, X., Cao, J.: Stochastic synchronization of coupled neural networks with intermittent control. Phys. Lett. A 373, 3259–3272 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Liang, Y., Wang, X.: Synchronization in complex networks with non-delay and delay couplings via intermittent control with two switched periods. Phys. A 395, 434–444 (2014)

    Article  MathSciNet  Google Scholar 

  30. Zhang, G., Shen, Y.: Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control. Neural Netw. 55, 1–10 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  31. Wang, H., Han, Z., Xie, Q., Zhang, W.: Finite-time chaos synchronization of unified chaotic system with uncertain parameters. Commun. Nonlinear Sci. Numer. Simul. 14, 2239–2247 (2009)

    Article  Google Scholar 

  32. Liu, X., Yu, W., Cao, J., Alsaadi, F.: Finite-time synchronisation control of complex networks via non-smooth analysis. IET Control Theory Appl. 9, 1245–1253 (2015)

    Article  MathSciNet  Google Scholar 

  33. Xu, R., Kao, Y., Gao, M.: Finite-time synchronization of Markovian jump complex networks with generally uncertain transition rates. Trans. Inst. Meas. Control 0142331215600046 (2015)

  34. Li, D., Cao, J.: Finite-time synchronization of coupled networks with one single time-varying delay coupling. Neurocomputing 166, 265–270 (2015)

    Article  Google Scholar 

  35. Yang, X., Wu, Z., Cao, J.: Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlinear Dyn. 73, 2313–2327 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  36. Liu, X., Park, J., Jiang, N., Cao, J.: Nonsmooth finite-time stabilization of neural networks with discontinuous activations. Neural Netw. 52, 25–32 (2014)

    Article  MATH  Google Scholar 

  37. Yin, J., Khoo, S., Man, Z., Yu, X.: Finite-time stability and instability of stochastic nonlinear systems. Automatica 47, 2671–2677 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  38. Yang, X., Cao, J.: Finite-time stochastic synchronization of complex networks. Appl. Math. Model. 34, 3631–3641 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  39. Mei, J., Jiang, M., Xu, W., Wang, B.: Finite-time synchronization control of complex dynamical networks with time delay. Commun. Nonlinear Sci. Numer. Simul. 18, 2462–2478 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  40. Li, B.: Finite-time synchronization for complex dynamical networks with hybrid coupling and time-varying delay. Nonlinear Dyn. 76, 1603–1610 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  41. Sun, Y., Li, W., Zhao, D.: Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies. Chaos 22, 023152 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  42. Mei, J., Jiang, M., Wu, Z., Wang, X.: Periodically intermittent controlling for finite-time synchronization of complex dynamical networks. Nonlinear Dyn. 79, 295–305 (2015)

    Article  MATH  Google Scholar 

  43. Xiong, W., Yu, W., Lü, J., Yu, X.: Fuzzy modelling and consensus of nonlinear multiagent systems with variable structure. IEEE Trans. Circuits Syst. I(61), 1183–1191 (2014)

    Article  Google Scholar 

  44. Yu, H., Shen, Y., Xia, X.: Adaptive finite-time consensus in multi-agent networks. Syst. Control Lett. 62, 880–889 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  45. Huang, J., Wen, C., Wang, W., Song, Y.: Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems. Automatica 51, 292–301 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  46. Cao, Y., Ren, W.: Finite-time consensus for multi-agent networks with unknown inherent nonlinear dynamics. Automatica 50, 2648–2656 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  47. Wu, J., Jiao, L.: Synchronization in complex delayed dynamical networks with nonsymmetric coupling. Phys. A 386, 513–530 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ1501002), the support of the National Natural Science Foundation of China (61174216, 61273183) and the Youth Fund of Chongqing Three Gorges University under Grant No. 14QN22.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, China

    Liangliang Li & Zhengwen Tu

  2. Department of Electrical, Electronic and Computer Engineering, Centre of New Energy Systems, University of Pretoria, Pretoria, 0028, South Africa

    Jun Mei

  3. College of Science, China Three Gorges University, Yichang, 443002, Hubei, China

    Jigui Jian

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  1. Liangliang Li
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Correspondence to Liangliang Li.

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Li, L., Tu, Z., Mei, J. et al. Finite-time synchronization of complex delayed networks via intermittent control with multiple switched periods. Nonlinear Dyn 85, 375–388 (2016). https://doi.org/10.1007/s11071-016-2692-6

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