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Generation of lag outer synchronization of complex networks with noise coupling

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Abstract

In this paper, we investigate the lag outer synchronization problem of complex dynamical networks with noise coupling. Based on the stability theory of stochastic differential equations, we obtain the sufficient conditions for the lag outer synchronization. The theoretical results show that the lag outer synchronization could be achieved only via white noise-based coupling. Furthermore, we show that noise can also be used to enhance the lag outer synchronization between two networks when two networks have both conventional linear coupling and white noise-based coupling. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

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References

  1. Pecora, L.M., Carroll, T.L.: Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80(10), 2109–2112 (1998)

    Article  Google Scholar 

  2. Wang, X.F., Chen, G.: Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans. Circ. Syst. I. Fundam. Theory Appl. 49(1), 54–62 (2002)

    Article  Google Scholar 

  3. Nishikawa, T., Motter, A.E., Lai, Y.C., Hoppensteadt, F.C.: Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? Phys. Rev. Lett. 91(1), 014101 (2003)

    Article  Google Scholar 

  4. Arenas, A., Daz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Phys. Rep. 469(3), 93–153 (2008)

    Article  MathSciNet  Google Scholar 

  5. Xu, Y.H., Yang, H.Z., Tong, D.B., Wang, Y.L.: Adaptive exponential synchronization in pth moment for stochastic time varying multi-delayed complex networks. Nonlinear Dyn. 73(3), 1423–1431 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  6. 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  MATH  MathSciNet  Google Scholar 

  7. Zhou, J.P., Wang, Z., Wang, Y.Y., Kong, Q.K.: Synchronization in complex dynamical networks with interval time-varying coupling delays. Nonlinear Dyn. 72(1–2), 377–388 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lü, J.H., Yu, X.H., Chen, G.R.: Chaos synchronization of general complex dynamical networks. Phys. A 334(1–2), 281–302 (2004)

    Article  MathSciNet  Google Scholar 

  9. Li, X., Wang, X., Chen, G.: Pinning a complex dynamical network to its equilibrium. IEEE Trans. Circ. Syst. I 51, 2074–2087 (2004)

    Article  MathSciNet  Google Scholar 

  10. Zhou, C., Motter, A.E., Kurths, J.: Universality in the synchronization of weighted random networks. Phys. Rev. Lett. 96(3), 034101–034104 (2006)

    Article  Google Scholar 

  11. Yu, W.W., Chen, G.R., Lü, J.H.: On pinning synchronization of complex dynamical networks. Automatica 45(2), 429–435 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Klovdahl, A.S.: Social networks and the spread of infectious diseases: the AIDS example. Soc. Sci. Med. 21(11), 1203–1216 (1985)

    Article  Google Scholar 

  13. Begon, M., Townsend, C., Harper, J.: Ecology: Individuals, Populations and Communities. Blackwell, London (1996)

    Book  Google Scholar 

  14. Wang, J., Zhang, J., Yuan, Z., Chen, A., Zhou, T.: Neurotransmitter-mediated collective rhythms in grouped Drosophila circadian clocks. J. Biol. Rhythm. 23(6), 472–482 (2008)

    Article  Google Scholar 

  15. Li, C.P., Sun, W.G., Kurths, J.: Synchronization between two coupled complex networks. Phys. Rev. E 76(4), 046204 (2007)

    Article  Google Scholar 

  16. Li, C.P., Xu, C.X., Sun, W.G., Xu, J., Kurths, J.: Outer synchronization of coupled discrete-time networks. Chaos 19(1), 013106 (2009)

    Article  MathSciNet  Google Scholar 

  17. Tang, H.W., Chen, L., Lu, J.A., Tse, C.K.: Adaptive synchronization between two complex networks with nonidentical topological structures. Phys. A 387(22), 5623–5630 (2008)

    Article  Google Scholar 

  18. Sun, Y.Z., Li, W., Zhao, D.H.: Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies. Chaos 22(2), 023152–023158 (2012)

    Article  MathSciNet  Google Scholar 

  19. Sun, Y.Z., Zhao, D.H.: Effects of noise on the outer synchronization of two unidirectionally coupled complex dynamical networks. Chaos 22(2), 023131–023140 (2012)

    Article  MathSciNet  Google Scholar 

  20. Sun, Y.Z., Li, W., Ruan, J.: Finite-time generalized outer synchronization between two different complex networks. Commun. Theor. Phys. 58(5), 697–703 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  21. Wu, X., Zheng, W.X., Zhou, J.: Generalized outer synchronization between complex dynamical networks. Chaos 19(1), 013109–013117 (2009)

    Article  MathSciNet  Google Scholar 

  22. Wang, J.W., Ma, Q., Zeng, L., Abd-Elouahab, M.S.: Mixed outer synchronization of coupled complex networks with time-varying coupling delay. Chaos 21(1), 013121–013128 (2011)

    Article  MathSciNet  Google Scholar 

  23. Wu, Y.Q., Li, C.P., Wu, Y.J., Kurths, J.: Generalized synchronization between two different complex networks. Commun. Nonlinear Sci. Numer. Simul. 17(1), 349–355 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  24. Yang, Z.Q., Zhang, Q., Chen, Z.Q.: Adaptive linear generalized synchronization between two nonidentical networks. Commun. Nonlinear Sci. Numer. Simul. 17(6), 2628–2636 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  25. Porfiri, M., di Bernardo, M.: Criteria for global pinning-controllability of complex networks. Automatica 44(12), 3100–3106 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  26. Zheng, S., Dong, G.G., Bi, Q.S.: Impulsive synchronization of complex networks with non-delayed and delayed coupling. Phys. Lett. A 373(46), 4255–4259 (2009)

    Article  MATH  Google Scholar 

  27. Mahdavi, N., Menhaj, M.B., Kurths, J., Lu, J.Q., Afshar, A.: Pinning impulsive synchronization of complex dynamical networks. Int. J. Bifurc. Chaos 22(10), 1250239 (2012)

    Article  MathSciNet  Google Scholar 

  28. Xia, W.G., Cao, J.D.: Pinning synchronization of delayed dynamical networks via periodically intermittent control. Chaos 19(1), 013120 (2009)

    Article  MathSciNet  Google Scholar 

  29. Cai, S.M., Liu, Z.R., Xu, F.D., Shen, J.W.: Periodically intermittent controlling complex dynamical networks with time-varying delays to a desired orbit. Phys. Lett. A 373(42), 3846–3854 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  30. Lin, W., He, Y.B.: Complete synchronization of the noise-perturbed Chua’s circuits. Chaos 15(2), 023705–023713 (2005)

    Article  Google Scholar 

  31. Cao, J.D., Wang, Z.D., Sun, Y.H.: Synchronization in an array of linearly stochastically coupled networks with time delay. Phys. A 385(2), 718–728 (2007)

    Article  MathSciNet  Google Scholar 

  32. Wang, G.P., Jin, W.Y., Hu, C.B.: The complete synchronization of Morris–Lecar neurons influenced by noise. Nonlinear Dyn. 73(3), 1715–1719 (2013)

    Article  MathSciNet  Google Scholar 

  33. Sun, Y.Z., Li, W., Ruan, J.: Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation. Commun. Nonlinear Sci. Numer. Simul. 18(4), 989–998 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  34. Lin, W., Chen, G.R.: Using white noise to enhance synchronization of coupled chaotic systems. Chaos 16(1), 013134 (2006)

    Article  MathSciNet  Google Scholar 

  35. Xiao, Y.Z., Xu, W., Li, X.C., Tang, S.F.: The effect of noise on the complete synchronization of two bidirectionally coupled piecewise linear chaotic systems. Chaos 19(1), 013131 (2009)

    Article  MathSciNet  Google Scholar 

  36. Nagail, K.H., Kori, H.: Noise-induced synchronization of a large population of globally coupled nonidentical oscillators. Phys. Rev. E 81(1), 065202 (2010)

    Article  Google Scholar 

  37. Xiao, Y.Z., Tang, S.F., Xu, Y.: Theoretical analysis of multiplicative-noise-induced complete synchronization in global coupled dynamical network. Chaos 22(1), 013110–013116 (2012)

  38. Li, C.G., Chen, G.R.: Synchronization in general complex dynamical networks with coupling delays. Phys. A 343(15), 263–278 (2004)

    Article  MathSciNet  Google Scholar 

  39. Lu, W.H., Chen, T.P., Chen, G.R.: Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay. Phys. D 221(2), 118–134 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  40. Xu, S., Lam, J.: A survey of linear matrix inequality techniques in stability analysis of delay systems. Int. J. Syst. Sci. 39, 1095–1113 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  41. Wu, W., Chen, T.P.: Global synchronization criteria of linearly coupled neural network systems with time-varying coupling. IEEE Trans. Neural Netw. 19(2), 319–332 (2008)

    Article  Google Scholar 

  42. Wang, Q., Chen, G., Perc, M.: Synchronization bursts on scale-free neuronal networks with attractive and repulsive coupling. PloS One 6, e15851 (2011)

    Article  Google Scholar 

  43. Balasubramaniam, P., Chandran, R., Jeeva Sathya Theesar, S.: Synchronization of chaotic nonlinear continuous neural networks with time-varying delay. Cogn. Neurodyn. 5(4), 361–371 (2011)

    Article  Google Scholar 

  44. Balasubramaniam, P., Vembarasan, V.: Synchronization of recurrent neural networks with mixed time-delays via output coupling with delayed feedback. Nonlinear Dyn. 70(1), 667–691 (2012)

    Article  MathSciNet  Google Scholar 

  45. Guo, W.L., Austin, F., Chen, S.H., Sun, W.: Pinning synchronization of the complex networks with non-delayed and delayed coupling. Phys. Lett. A 373(17), 1565–1572 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  46. Heisler, I.A., Braun, T., Zhang, Y., Hu, G., Cerdeira, H.A.: Experimental investigation of partial synchronization in coupled chaotic oscillators. Chaos 13(1), 185–194 (2003)

    Article  Google Scholar 

  47. Chua, L.O., Wu, C.W., Huang, A., Zhong, G.Q.: A universal circuit for studying and generating chaos. I. Routes to chaos. IEEE Trans. Circuits Syst. I. Fundam. Theory Appl. 40(10), 732–744 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  48. Mao, X.: Stochastic Differential Equations and Applications. Horwood, England (1997)

    MATH  Google Scholar 

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Acknowledgments

The authors are very grateful to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 61403393) and the Fundamental Research Funds for the Central Universities (Grant No. 2014QNB34).

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Authors and Affiliations

  1. School of Science, China University of Mining and Technology, Xuzhou, 221008, People’s Republic of China

    Hongjun Shi, Yongzheng Sun & Lianying Miao

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  1. Hongjun Shi
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  2. Yongzheng Sun
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Correspondence to Yongzheng Sun.

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Shi, H., Sun, Y. & Miao, L. Generation of lag outer synchronization of complex networks with noise coupling. Nonlinear Dyn 79, 1131–1140 (2015). https://doi.org/10.1007/s11071-014-1728-z

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