Skip to main content
SpringerLink
Log in

Inter network synchronisation of complex dynamical networks by using smooth proportional integral SMC technique

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

This paper puts forward the inter network synchronisation of complex dynamical networks (CDNs) using drive-response philosophy. The inter networks consist of a drive network (each node represents a hyperchaotic system) and a response network (consists of chaotic system at each node). Synchronisation is achieved using a novel proportional integral (PI) based sliding mode control (SMC) scheme and inter network synchronisation criterion is derived. Unlike the conventional SMC technique, the proposed proportional integral-sliding mode control (PI-SMC) technique does not result decoupled error dynamics. A smooth switching surface is designed to eliminate the chattering effect. The different network configurations: small-world and scale-free networks, are simulated and the simulation results show that the proposed synchronisation scheme is effective for the inter network synchronisation between two or more CDNs. The effect of relevant parameters on the synchronisation process in the Watts-Strogatz (WS) small-world and Barabasi-Albert (BA) scale-free networks are analysed. Finally, the proposed PI-SMC technique is compared with standard SMC technique to justify the advantages over the standard SMC technique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Erdos, A. Renyi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1957)

    Google Scholar 

  2. D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)

    Article  ADS  Google Scholar 

  3. D.J. Watts,The dynamics of networks between order and randomness (Princeton University Press, Princeton, 1999), pp. 211–284

  4. A.L. Barabasi, R. Albert, Science 286, 509 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  5. A.L. Barabasi, R. Albert, H. Jeong, Physica A 272, 173 (1999)

    Article  ADS  Google Scholar 

  6. R. Albert, A.L. Barabasi, Rev. Mod. Phys. 74, 47 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  7. X.F. Wang, G. Chen, Int. J. Bifurc. Chaos 12, 187 (2002)

    Article  Google Scholar 

  8. X.F. Wang, G. Chen, IEEE Trans. Circuits Syst. 49, 54 (2002)

    Article  Google Scholar 

  9. M. Barahona, L.M. Pecora, Phys. Rev. Lett. 5, 54 (2002)

    Google Scholar 

  10. P. Crucitti, V. Latora, M. Marchiori, A. Rapisarda, Physica A 320, 622 (2003)

    Article  ADS  Google Scholar 

  11. P. Crucitti, V. Latora, M. Marchiori, A. Rapisarda, Physica A 340, 388 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  12. X.F. Wang, G. Chen, IEEE Circuits Syst. Mag. 3, 6 (2003)

    Article  Google Scholar 

  13. J.L. Hu, H. Leung, G. Chen, Dyn. Contin. Discrete Impuls. Syst. 11, 70 (2004)

    Google Scholar 

  14. J. Lu, X. Yu, G. Chen, Physica A 334, 281 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  15. X. Li, G. Chen, IEEE Trans. Circuits Syst. 50, 1381 (2005)

    Google Scholar 

  16. J. Zhao, D.J. Hill, T. Liu, Automatica 45, 2502 (2009)

    Article  Google Scholar 

  17. D. Zhang, J. Xu, Appl. Math. Comput. 217, 164 (2010)

    MathSciNet  Google Scholar 

  18. Y.Q. Che, J. Wang, K.M. Tsang, W.L. Chan, Nonlinear Anal. 11, 1096 (2010)

    Article  Google Scholar 

  19. P.P. Menon, C. Edwards, inProceedings of the 18th World Congress of International Federation of Automatic Control (IFAC), Milano, Italy, 2011, Vol. 18

  20. P.P. Singh, B.K. Roy, H. Handa, inAnnual IEEE India Conference (INDICON), Mumbai, India, 2013, Vol. 10

  21. X.Z. Jin, J.H. Park, Inf. Sci. 274, 273 (2014)

    Article  Google Scholar 

  22. Y. Xiao, S. Tang, X. Yang, Appl. Math. Model. 38, 4148 (2014)

    Article  MathSciNet  Google Scholar 

  23. Y. Ma, Y. Zheng, Neurocomputing 168, 626 (2015)

    Article  Google Scholar 

  24. T. Jing, F. Chen, X. Zhang, Neurocomputing 199, 178 (2016)

    Article  Google Scholar 

  25. J.H. Zhu, G.H. Yang, Neurocomputing 175, 287 (2016)

    Article  Google Scholar 

  26. S.H. Lee, M.J. Park, O.M. Kwon, R. Sakthivel, Inf. Sci. 420, 454 (2017)

    Article  Google Scholar 

  27. Y. Miao, H. Liang, Z. Haiyun, C. Zhigang, Y. Junyan, Math. Probl. Eng. 2017, 11 (2017)

    Google Scholar 

  28. L. Su, D. Ye, X. Yang, J. Franklin Inst. 354, 6855 (2017)

    Article  MathSciNet  Google Scholar 

  29. A. Muhammadhaji, A. Abdurahman, H. Jiang, J. Control Sci. Eng. 2017, 13 (2017)

    Article  Google Scholar 

  30. J. Fang, N. Liu, J. Sun, Math. Prob. Eng. 2018, 11 (2018)

    Google Scholar 

  31. T. Yu, M. Su, Trans. Inst. Meas. Control 41, 540 (2019)

    Article  Google Scholar 

  32. G. Chen, X. Dong,From chaos to order: methodologies, perspectives and applications (World Scientific, Singapore, 1998), pp. 311–387

  33. V. Latora, M. Baranger, A. Rapisarda, C. Tsallis, Phys. Lett. A 273, 97 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  34. P.P. Singh, K.M. Singh, B.K. Roy, Eur. Phys. J. Special Topics 227, 731 (2018)

    Article  ADS  Google Scholar 

  35. P.P. Singh, B.K. Roy, Ann. Rev. Control 45, 152 (2018)

    Article  Google Scholar 

  36. S. Banerjee, L. Rondoni, M. Mitra, inApplications of Chaos and Nonlinear Dynamics in Science and Engineering (Springer, Berlin, 2015), Vol. 3, pp. 371–392

  37. S. Mukherjee, S.K. Palit, S. Banerjee, M.R. K. Ariffin, L. Rondoni, D.K. Bhattacharya, Physica A 439, 93 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  38. P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 8, 995 (2015)

    Google Scholar 

  39. S. Banerjee, J. Kurths, Eur. Phys. J. Special Topics 223, 1441 (2014)

    Article  ADS  Google Scholar 

  40. P.P. Singh, J.P. Singh, B.K. Roy, IETE J. Res. 63, 853 (2017)

    Article  Google Scholar 

  41. P.P. Singh, B.K. Roy, Eur. Phys. J. Special Topics 228, 169 (2019)

    Article  ADS  Google Scholar 

  42. P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 9, 171 (2016)

    Google Scholar 

  43. P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 9, 159 (2016)

    Google Scholar 

  44. P.P. Singh, J.P. Singh, B.K. Roy, Chaos Solitons Fractals 69, 31 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  45. Z. Wei, R. Wang, A. Liu, Math. Comp. Simul. 100, 13 (2014)

    Article  Google Scholar 

  46. Z. Wei, W. Zhang, Z. Wang, M. Yao, Inter. J. Bifurc. Chaos 25, 1550028 (2015)

    Article  Google Scholar 

  47. Z. Wei, P. Yu, W. Zhang, M. Yao, Nonlinear Dyn. 82, 131 (2015)

    Article  Google Scholar 

  48. Z. Wei, I. Moroz, J.C. Sprott, A. Akgul, W. Zhang, Chaos 27, 033101 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  49. Y. Feng, J. Pu, Z. Wei, Eur. Phys. J. Special Topics 224, 1593 (2015)

    Article  ADS  Google Scholar 

  50. Y. Li, Z. Wei, W. Zhang, M. Perc, R. Repnik, Appl. Math. Comput. 354, 180 (2019)

    MathSciNet  Google Scholar 

  51. B.C. Bao, Z. Liu, Chin. Phys. Lett. 25, 2396 (2008)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, National Institute of Technology Meghalaya, Shillong, 793003, Meghalaya, India

    Piyush Pratap Singh

  2. Department of Electrical Engineering, National Institute of Technology, Silchar, 788010, Assam, India

    Binoy Krishna Roy

Authors
  1. Piyush Pratap Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Binoy Krishna Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Piyush Pratap Singh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, P.P., Roy, B.K. Inter network synchronisation of complex dynamical networks by using smooth proportional integral SMC technique. Eur. Phys. J. Spec. Top. 229, 861–876 (2020). https://doi.org/10.1140/epjst/e2020-900149-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2020-900149-3

Search

Navigation