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Multiswitching combination synchronisation of non-identical fractional-order chaotic systems

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Abstract

In this paper, multiswitching combination synchronisation (MSCS) scheme has been investigated in a class of three non-identical fractional-order chaotic systems. The fractional-order Lorenz and Chen systems are taken as the drive systems. The combination of multidrive systems is then synchronised with the fractional-order Lü chaotic system. In MSCS, the state variables of the two drive systems synchronise with different state variables of the response system, simultaneously. Based on the stability of fractional-order chaotic systems, the MSCS of three fractional-order non-identical systems has been investigated. For the synchronisation of three non-identical fractional-order chaotic systems, suitable controllers have been designed. Theoretical analysis and numerical results are presented to demonstrate the validity and feasibility of the applied method.

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References

  1. I Podlubny, Fractional differential equations (Academic Press, New York, 1999)

    MATH  Google Scholar 

  2. R Hilfer, Applications of fractional calculus in physics (World Scientific, 2000)

  3. R Caponetto, J J Trujillo and J A T Machado, Mathematical problems in engineering (2016)

  4. K A Lazopoulos, D Karaoulanis and A K Lazopoulos, Mech. Res. Commun. 78, 1–5, (2016)

    Article  Google Scholar 

  5. A H Bhrawy and M A Zaky, Appl. Math. Model. 40(2), 832 (2016)

    Article  MathSciNet  Google Scholar 

  6. R P Agarwal, A M El-Sayed and S M Salman, Adv. Differ. Equ. 1(1) (2013)

    Google Scholar 

  7. C Li and G Chen, Physica A 341, 55 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  8. C Li and G Peng, Chaos Solitons Fractals 22(2), 443 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  9. W H Deng and C P Li, Physica A 353, 61 (2005)

    Article  ADS  Google Scholar 

  10. Z M Ge and C Y Ou, Chaos Solitons Fractals 34(2), 262 (2007)

    Article  ADS  Google Scholar 

  11. L M Pecora and T L Carroll, Phys. Rev. Lett. 64(8), 821 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  12. A Khan and Shikha, Int. J. Dynam. Control, https://doi.org/10.1007/s40435-017-0339-1 (2017)

  13. L Chen, R Wu, Y He and Y Chai, Nonlinear Dynam. 80(1–2), 51 (2015)

    Article  MathSciNet  Google Scholar 

  14. X Lin, S Zhou and H Li, Int. J. Bifurc. Chaos 26(03), 1650046 (2016)

    Article  Google Scholar 

  15. A Khan and Shikha, Int. J. Dyn. Control 5(4), 1114 (2017)

    Article  MathSciNet  Google Scholar 

  16. A Khan and M A Bhat, Nonlinear Dyn. Syst. Theory 16(4), 350 (2016)

    MathSciNet  Google Scholar 

  17. N F Rulkov, M M Sushchik, L S Tsimring and H D Abarbanel, Phys. Rev. E 51(2), 980 (1995)

    Article  ADS  Google Scholar 

  18. R Mainieri and J Rehacek, Phys. Rev. Lett. 82(15), 3042 (1999)

    Article  ADS  Google Scholar 

  19. A Khan and M A Bhat, Comput. Math. Model. 28(4), 517 (2017)

  20. A Khan and S Shikha, Int. J. Nonlinear Sci. 22(1), 44 (2016)

    MathSciNet  Google Scholar 

  21. L Runzi, W Yinglan and D Shucheng, Chaos 21(4), 043 (2011)

    Article  Google Scholar 

  22. L Runzi and W Yinglan, Chaos 22(2), 023 (2012)

    Article  Google Scholar 

  23. J Sun, Y Shen, Q Yin and C Xu, Chaos 23(1), 013 (2013)

    Article  Google Scholar 

  24. J Sun, Q Yin and Y Shen, Europhys. Lett. 106(4), 40005 (2014)

    Article  ADS  Google Scholar 

  25. A Wu and J Zhang, Adv. Differ. Equ. 1(1), 228 (2014).

  26. J Sun, Y Shen, G Zhang, C Xu and G Cui, Nonlinear Dyn. 73(3), 1211 (2013)

    Article  Google Scholar 

  27. A Khan and M A Bhat, Math. Meth. Appl. Sci. 40(15), 5654 (2017)

  28. B Zhang and F Deng, Nonlinear Dyn. 77(4), 1519 (2014)

    Article  Google Scholar 

  29. K S Ojo, A N Njah and O I Olusola, Arch. Control Sci. 25(4), 463 (2015)

    Article  MathSciNet  Google Scholar 

  30. A Ucar, K E Lonngren and E W Bai, Chaos Solitons Fractals 38(1), 254 (2008)

  31. M A Bhat and A Khan, Int. J. Model. Simul., https://doi.org/10.1080/02286203.2018.1442988(2018)

  32. A Khan and M A Bhat, Int. J. Dynam. Control 5(4), 1211 (2017)

    Article  Google Scholar 

  33. A Khan and M A Bhat, J. Uncertain Sys. 11 (2017)

  34. M Caputo, Geophys. J. Int. 13(5), 529 (1967)

    Article  ADS  Google Scholar 

  35. K Diethelm and N J Ford, J. Math. Anal. Appl. 265(2), 229 (2002)

    Article  MathSciNet  Google Scholar 

  36. D Matignon, Comput. Engng Syst. Appl. 2, 963 (1996)

    Google Scholar 

  37. Y Yu, H X Li, S Wang and J Yu, Chaos Solitons Fractals 42(2), 1181 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  38. C Li and G Chen, Chaos Solitons Fractals 22(3), 549 (2004)

    Article  ADS  Google Scholar 

  39. J G Lu, Phys. Lett. A 354(4), 305 (2006)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, New Delhi, 110 025, India

    Muzaffar Ahmad Bhat & Ayub Khan

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  1. Muzaffar Ahmad Bhat
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  2. Ayub Khan
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Correspondence to Muzaffar Ahmad Bhat.

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Bhat, M.A., Khan, A. Multiswitching combination synchronisation of non-identical fractional-order chaotic systems. Pramana - J Phys 90, 73 (2018). https://doi.org/10.1007/s12043-018-1560-y

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  • DOI: https://doi.org/10.1007/s12043-018-1560-y

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