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Adaptive synchronization of coupled nonidentical chaotic systems with complex variables and stochastic perturbations

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Abstract

This paper considers asymptotic synchronization in an array of complex-variable chaotic systems, where node systems exhibit nonidentical nonlinear dynamics and subject to different stochastic perturbations. The effects of the differences among the node systems are overcome by designing a special adaptive discontinuous controller. By using Lyapunov stability theorem and stochastic properties, sufficient conditions are obtained to guarantee the synchronization. Finally, numerical simulations are given to show the effectiveness of the theoretical results.

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References

  1. Liao, T.L., Huang, N.S.: An observer-based approach for chaotic synchronization with applications to secure communications. IEEE Trans. Circuits Syst. I 46(9), 1144–1150 (1999)

    Article  MATH  Google Scholar 

  2. Yang, X.S., Cao, J.D.: Stochastic synchronization of coupled neural networks with intermittent control. Phys. Lett. A 373(36), 3259–3272 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Strogatz, S.H., Stewart, I.: Coupled oscillators and biological synchronization. Sci. Am. 269(6), 102–109 (1993)

    Article  Google Scholar 

  4. Ma, J., Song, X., Jin, W., Wang, C.: Autapse-induced synchronization in a coupled neuronal network. Chaos Solitons Fractals 80, 31–38 (2015)

    Article  MathSciNet  Google Scholar 

  5. Abeles, M., Prut, Y., Bergman, H., Vaadia, E.: Synchronization in neuronal transmission and its importance for information processing. Prog. Brain Res. 102, 395–404 (1994)

    Article  Google Scholar 

  6. Yang, X.S., Yang, Z.C., Nie, X.B.: Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication. Commun. Nonlinear Sci. Numer. Simul. 19(5), 1529–1543 (2014)

    Article  MathSciNet  Google Scholar 

  7. Kristian, H.M., Frank, L.L., Michael, S.: Distributed static output-feedback control for state synchronization in networks of identical LTI systems. Automatica 53, 282–290 (2015)

    Article  MathSciNet  Google Scholar 

  8. Jin, X.Z., Yang, G.H.: Robust synchronization control for complex networks with disturbed sampling couplings. Commun. Nonlinear Sci. Numer. Simul. 19(6), 1985–1995 (2014)

    Article  MathSciNet  Google Scholar 

  9. Yang, X.S., Wu, Z.Y., Cao, J.D.: Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlinear Dyn. 73(4), 2313–2327 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sun, H.Y., Li, N., Zhao, D.P., Zhang, Q.L.: Synchronization of complex networks with coupling delays via adaptive pinning intermittent control. Int. J. Autom. Comput. 10(4), 312–318 (2013)

    Article  Google Scholar 

  11. Ma, J., Zhang, A.H., Xia, Y.F., et al.: Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems. Appl. Math. Comput. 215(9), 3318–3326 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Yang, X.S., Cao, J.D., Long, Y., Rui, W.R.: Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations. IEEE Trans. Neural Netw. 21(10), 1656–1667 (2010)

    Article  Google Scholar 

  13. Tanaka, G., Aihara, K.: Complex-valued multistate associative memory with nonlinear multilevel functions for gray-level image reconstruction. IEEE Trans. Neural Netw. 20(9), 1463–1473 (2009)

    Article  Google Scholar 

  14. Tripathi, B.K., Kalra, P.K.: On efficient learning machine with root-power mean neuron in complex domain. IEEE Trans. Neural Netw. 22(5), 727–738 (2011)

    Article  Google Scholar 

  15. André, R.B., Dalcimar, C., Odemir, M.B.: Texture analysis and classification: a complex network-based approach. Inf Sci 219(10), 168–180 (2013)

    Google Scholar 

  16. Wu, Z.Y., Duan, J.Q., Fu, X.C.: Complex projective synchronization in coupled chaotic complex dynamical systems. Nonlinear Dyn. 69, 771–779 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu, P., Liu, S.T.: Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances. Nonlinear Dyn. 70(1), 585–599 (2012)

    Article  MathSciNet  Google Scholar 

  18. Sun, J.W., Cui, G.Z., Wang, Y.F., Shen, Y.: Combination complex synchronization of three chaotic complex systems. Nonlinear Dyn. 79(2), 953–965 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu, D.F., Wu, Z.Y., Ye, Q.L.: Adaptive impulsive synchronization of uncertain drive-response complex-variable chaotic systems. Nonlinear Dyn. 75, 209–216 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhao, J., Hill, D.J., Liu, T.: Synchronization of dynamical networks with nonidentical nodes: criteria and control. IEEE Trans. Circuits Syst. I 58(3), 584–594 (2011)

    Article  MathSciNet  Google Scholar 

  21. Lu, W.L., Liu, B., Chen, T.P.: Cluster synchronization in networks of coupled nonidentical dynamical systems. Chaos 20(1), 013120 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  23. Salarieh, H., Alasty, A.: Adaptive synchronization of two chaotic systems with stochastic unknown parameters. Commun. Nonlinear Sci. Numer. Simul. 14(2), 508–519 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Mahmoud, G.M., Bountis, T., Mahmoud, E.E.: Active control and global synchronization of the complex Chen and Lü systems. Int. J. Bifurc. Chaos 17(12), 4295–4308 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Aly, S., Qahtani, A.A., Khenous, H.B., Mahmoud, G.: Impulsive control and synchronization of complex Lorenz systems. Abstract and Applied Analysis. art. ID: 932327 (2014)

  26. Wu, Z.Y., Liu, D.F., Ye, Q.L.: Pinning impulsive synchronization of complex-variable dynamical network. Commun. Nonlinear Sci. Numer. Simul. 20(1), 273–280 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (NSFC) (Grant No. 61263020).

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Authors and Affiliations

  1. Department of Mathematics, Chongqing Normal University, Chongqing, 401331, China

    Enli Wu & Xinsong Yang

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  1. Enli Wu
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  2. Xinsong Yang
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Correspondence to Xinsong Yang.

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Wu, E., Yang, X. Adaptive synchronization of coupled nonidentical chaotic systems with complex variables and stochastic perturbations. Nonlinear Dyn 84, 261–269 (2016). https://doi.org/10.1007/s11071-015-2433-2

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