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Synchronization of coupled delayed switched neural networks with impulsive time window

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Abstract

Synchronization of coupled delayed switched neural networks (DSNNs) with impulsive time window is one of the most challenging problems in the field of complex networks. In this paper, some sufficient conditions ensuring the synchronization of coupled DSNNs with all subsystems self-synchronizing are presented. Then this results are extended to the following two cases: all subsystems are desynchronizing and some of subsystems are self-synchronizing. By applying switching Lyapunov function method, some general criteria which characterize the impulse and switching effects in aggregated form are given. Moreover, from our results, one can easily observes that the impulsive time window control strategy is more general and more applicable than the fixed impulses controllers. Finally, numerical simulations are presented to further demonstrate the effectiveness of the proposed results.

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References

  1. Wen, S.P., Zeng, Z.G., Huang, T.W., Zhang, Y.D.: Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators. IEEE Trans. Fuzzy Syst, 22(6), 1704–1713 (2014)

    Article  Google Scholar 

  2. Wen, S.P., Huang, T.W., Zeng, Z.G., Chen, Y.R., Li, P.: Circuit design and exponential stabilization of memristive neural networks. Neural Netw. 63, 48–56 (2015)

    Article  MATH  Google Scholar 

  3. Song, X.L., Wang, C.N., Ma, J., Tang, J.: Transition of electric activity of neurons induced by chemical and electric autapses. Sci. China Technol. Sci. 58(6), 1007–1014 (2015)

    Article  Google Scholar 

  4. Wen, S.P., Zeng, Z.G., Huang, T.W., Meng, Q.G., Yao, W.: Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1493–1502 (2015)

    Article  Google Scholar 

  5. Zheng, S.: Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling. Nonlinear Dyn. 67(4), 2621–2630 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Sun, J., Shen, Y.: Quasi-ideal memory system. IEEE Trans. Cybern. 45(7), 1353–1362 (2014)

    Article  MathSciNet  Google Scholar 

  7. Zheng, S., Wang, S., Dong, G., Bi, Q.: Adaptive synchronization of two nonlinearly coupled complex dynamical networks with delayed coupling. Commun. Nonlinear Sci. Numer. Simul. 17(1), 284–291 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Qin, H.X., Ma, J., Jin, W.Y., Wang, C.N.: Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci. China Technol. Sci. 57(5), 936–946 (2014)

    Article  MathSciNet  Google Scholar 

  9. Sun, J., Yin, Q., Shen, Y.: Compound synchronization for four chaotic systems of integer order and fractional order. Europhys. Lett. 106(4), 40005 (2014)

    Article  Google Scholar 

  10. Zheng, S., Shao, W.: Mixed outer synchronization of dynamical networks with nonidentical nodes and output coupling. Nonlinear Dyn. 73(4), 2343–2352 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, H.Y., Shen, Y., Pan, Y.N., Lam, H.K.: Model reduction for interval Type-2 Takagi-Sugeno fuzzy systems. Automatica 61, 308–314 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sun, J., Shen, Y., Yin, Q., Xu, C.: Compound synchronization of four memristor chaotic oscillator systems and secure communication. Chaos: An Interdiscip. J Nonlinear Sci. 23(1), 013140 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Li, H.Y., Pan, Y.N., Zhou, Q.: Filter Design for interval Type-2 fuzzy systems with D stability constraints under a unified frame. IEEE Trans. Fuzzy Syst. 23(3), 719–725 (2015)

    Article  Google Scholar 

  14. Li, H.Y., Wu, C.W., Shi, p, Gao, Y.B.: Control of nonlinear networked systems with packet dropouts: interval Type-2 fuzzy model-based approach. IEEE Trans. Cybern. 45(11), 2378–2389 (2014)

    Article  Google Scholar 

  15. He, X., Li, C.D., Huang, T.W.: Bogdanov–Takens singularity in tri-neuron network with time delay. IEEE Trans. Neural Netw. Leran. Syst. 24(6), 1001–1007 (2013)

    Article  Google Scholar 

  16. Li, H.Q., Liao, X.F., Lei, X.Y.: Second-order consensus seeking in multi-agent systems with nonlinear dynamics over random switching directed network. IEEE Trans. Circuits Syst. I, Reg. Pap. 60(6), 1595–1607 (2013)

    Article  MathSciNet  Google Scholar 

  17. Wen, S.P., Huang, T.W., Yu, X., Chen, M.Z., Zeng, Z.G.: Aperiodic sampled-data sliding-mode control of fuzzy systems with communication delays via the event-triggered method. IEEE Trans. Fuzzy Syst. 2501412 (2015). doi:10.1109/TFUZZ.2015

  18. Zeng, Z.G., Huang, Y., Zheng, W.X.: Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function. IEEE Trans. Neural. Netw. Leran. Systemsv 21(8), 1371–1377 (2010)

    Article  Google Scholar 

  19. Zeng, Z.G., Wang, J., Liao, X.X.: Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 50(10), 1353–1358 (2003)

    Article  MathSciNet  Google Scholar 

  20. Zeng, Z.G., Zheng, W.X.: Multistability of two kinds of recurrent neural networks with activation functions symmetrical about the origin on the phase plan. IEEE Trans. Neural Netw. Leran. Syst. 24(11), 1749–1762 (2013)

    Article  Google Scholar 

  21. Tang, Y., Gao, H., Zou, W., Kurths, J.: Distributed synchronization in networks of agent systems with nonlinearities and random switchings. IEEE Trans. Cybern. 43(1), 358–370 (2013)

    Article  Google Scholar 

  22. Miao, Q., Tang, Y., Kurths, J., Fang, J.A., Wong, W.K.: Pinning controllability of complex networks with community structure. Chaos 23(3), 033114 (2013)

    Article  MATH  Google Scholar 

  23. Li, N., Cao, J.: Periodically intermittent control on robust exponential synchronization for switched interval coupled networks. Neurocomputing 131, 52–58 (2014)

    Article  Google Scholar 

  24. Hu, M., Cao, J., HU, J.A.: Mean square exponential stability for discrete-time stochastic switched static neural networks with randomly occurring nonlinearities and stochastic delay. Neurocomputing 129, 476–481 (2014)

    Article  Google Scholar 

  25. Strogatz, S.: Exploring complex networks. Nature 410, 268–276 (2001)

    Article  Google Scholar 

  26. Wu, X., Tang, Y., Cao, J., Zhang, W.B.: Distributed Consensus of Stochastic Delayed Multi-agent Systems Under Asynchronous Switching. IEEE Transaction On Cybernetics, (2015)

  27. Tang, Y., Gao, H., Zhang, W.B., Kurths, J.: Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses. Automatica 53, 346–354 (2015)

    Article  MathSciNet  Google Scholar 

  28. Lu, J.Q., Ho, D.W.C., Cao, J.D.: A unified synchronization criterion for impulsive dynamical networks. Automatica 46(7), 1215–1221 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  29. Yang, X.S., Cao, J.D., Lu, J.Q.: Synchronization of delayed complex dynamical networks with impulsive and stochastic effects. Nonlinear Anal.: Real Word Appl. 12, 2252–2266 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  30. Yang, X.S., Cao, J.D., Lu, J.Q.: Synchronization of randomly coupled neural networks with markovian jumping and time delay. IEEE Trans. Circuits Syst. I, Reg. Pap. 60(2), 363–376 (2013)

    Article  MathSciNet  Google Scholar 

  31. Zhang, W.B., Tang, Y., Wu, X.T., Fang, J.A.: Synchronization of nonlinear dynamical networks with heterogeneous impulses. IEEE Trans. Circuits Syst.-I: Regular Pap. 61(4), 1220–1228 (2014)

    Article  Google Scholar 

  32. Zhang, W.B., Tang, Y., Miao, Q.Y., Du, W.: Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. IEEE Trans. Neural. Netw Learn. Syst. 24(8), 1316–1326 (2013)

    Article  Google Scholar 

  33. Li, C.J., Yu, W.W., Huang, T.W.: Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach. Neural Netw. 54, 85–94 (2014)

    Article  MATH  Google Scholar 

  34. Li, C.J., Li, C.D., Liao, X.F., Huang, T.W.: Impulsive effects on stability of high-order BAM neural networks with time delays. Neurocomputing 74(10), 1541–1550 (2011)

    Article  Google Scholar 

  35. Zhang, W., Tang, Y., Wong, W.K., Miao, Q.: Stochastic stability of delayed neural networks with local impulsive effects. IEEE Trans. Neural Netw. Learn. Syst. 26(10), 2336–2345 (2014)

  36. Yang, X.S., Cao, J.D., Lu, J.Q.: Stochastic synchronization of complex networks with nonidentical node via hybrid adaptive and impulsive control. IEEE Trans. Circuits Syst. I, Reg. Pap. 59(2), 371–384 (2012)

    Article  MathSciNet  Google Scholar 

  37. Wong, W.K., Zhang, W.B., Tang, Y., Wu, X.T.: Stochastic synchronization of complex networks with mixed impulses. IEEE Trans. Circuits Syst. I, Reg. Pap. 60(10), 2657–2667 (2013)

    Article  MathSciNet  Google Scholar 

  38. Yang, Z.C., Xu, D.Y.: Stability analysis and design of impulsive control system with time delay. IEEE Trans. Autom. Control. 52(8), 1448–1454 (2007)

    Article  Google Scholar 

  39. Li, C.D., Feng, G., Huang, T.W.: On hybrid impulsive and switching neural networks. IEEE Trans. Syst. Man, Cybern. B: Cybern 38(6), 1549–1559 (2008)

    Article  Google Scholar 

  40. Yang, Z.C., Xu, D.Y.: Stability analysis of delay neural networks with impulsive effects. IEEE Trans. Circuits Syst. II, Express Briefs 52(8), 517–521 (2005)

    Article  Google Scholar 

  41. Li, X.D., Song, S.J.: Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Trans. Neural. Netw. Leran. Syst. 24(6), 868–877 (2013)

    Article  Google Scholar 

  42. Li, X.D.: Exponential stability of Cohen–Grossberg-type BAM neural networks with time-varying delays via impulsive control. Neurocomputing 73(1), 525–530 (2009)

    Article  Google Scholar 

  43. Li, X.D., Zhang, C.: Stability properties for Hopfield neural networks with delays and impulsive perturbations. Nonlinear Anal.: Real World Appl. 10(5), 3253–3265 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work is supported by Fundamental Research Funds for Central Universities (XDJK2015C075, SWU115014) and Natural Science Foundation Project of Chongqing CSTC (Grant No. cstc2015jcyjA40046), Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2015jcyjBX0052). This research also is supported by the Natural Science Foundation of China (Grant Nos: 61374078, 61302180) and NPRP grant # NPRP 4-1162-1-181 from the Qatar National Research Fund (a member of Qatar Foundation).

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Authors and Affiliations

  1. College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, People’s Republic of China

    Xin Wang & Chuandong Li

  2. Texas A & M University at Qatar, Doha, 23874, Qatar

    Tingwen Huang

  3. School of Mathematics Science, Chongqing Normal University, Chongqing, 401331, People’s Republic of China

    Hui Wang

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  1. Xin Wang
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Correspondence to Xin Wang.

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Wang, X., Wang, H., Li, C. et al. Synchronization of coupled delayed switched neural networks with impulsive time window. Nonlinear Dyn 84, 1747–1757 (2016). https://doi.org/10.1007/s11071-016-2602-y

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