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Multi-switching synchronization between T system and Liu system

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Abstract

In this paper, multi-switching synchronization between two chaotic systems with fully unknown parameters has been studied. The proposed scheme presents a generalized way to achieve different synchronizations for different switching states of two chaotic systems. Investigations are accomplished by using adaptive control method and Lyapunov stability theory. To analyze the proposed methodology, example of chaotic T system and Liu system have been considered. Theoretical results are validated by numerical simulations.

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References

  1. Lakshmanan M, Murali K (1996) Chaos in nonlinear oscillators: controlling and synchronization. World Scientific, Singapore

    Book  MATH  Google Scholar 

  2. Han SK, Kerrer C, Kuramoto Y (1995) Dephasing and bursting in coupled neural oscillators. Phys Rev Lett 75(17):3190–3193

    Article  Google Scholar 

  3. Blasius B, Huppert A, Stone L (1999) Complex dynamics and phase synchronization in spatially extended ecological system. Nature 399:354–359

    Article  Google Scholar 

  4. Garfinkel A, Spano ML, Ditto WL, Weiss JN (1992) Controlling cardiac chaos. Science 257(5074):1230–1235

    Article  Google Scholar 

  5. Shi Z, Hong S, Chen K (2008) Experimental study on tracking the state of analog Chua’s circuit with particle filter for chaos synchronization. Phys Lett A 372(34):5575–5580

    Article  Google Scholar 

  6. Feki M (2003) An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons Fractals 18(1):141–148

    Article  MathSciNet  MATH  Google Scholar 

  7. Murali K, Lakshmanan M (1998) Secure communication using a compound signal from generlaized synchronizable chaotic systems. Phy Rev Lett A 241(6):303–310

    Article  MATH  Google Scholar 

  8. Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824

    Article  MathSciNet  MATH  Google Scholar 

  9. Luo RZ, Wei ZM (2009) Adaptive function projective synchronization of unified chaotic systems with uncertain parameters. Chaos Solitons Fractals 42(2):1266–1272

    Article  MATH  Google Scholar 

  10. Rosenblum MG, Pikovsky AS, Kurths J (1997) From phase to lag synchronization in coupled chaotic oscilllators. Phys Rev Lett 78(22):4193–4196

    Article  Google Scholar 

  11. Rulkov NF, Sushchik MN, Tsimring LS, Abardanel HDI (1995) Generalized synchronization of chaos in directionally coupled chaotic system. Phy Rev E 51(2):980–994

  12. Mainieri R, Rehacek J (1999) Projective synchronization in three dimensional chaotic systems. Phys Rev Lett 82(15):3042–3045

    Article  Google Scholar 

  13. Shuai JW, Durand DM (1999) Phase synchronization in two coupled chaotic neurons. Phys Lett A 264(4):289–297

    Article  MathSciNet  MATH  Google Scholar 

  14. Wu A, Zhang J (2014) Compound synchronization of fourth order memristor oscillator. Adv Differ Equ 2014:100–106

    Article  MathSciNet  Google Scholar 

  15. Ahmad I, Shafiq M, Saaban AB, Ibrahim AB, Shahzad M (2016) Robust finite-time global synchronization of chaotic systems with different orders. Optik 127(19):8172–8185

    Article  Google Scholar 

  16. Ahmad I, Saaban AB, Ibrahim AB, Shahzad M, Alsawalha MM (2016) Reduced-order synchronization of time-delay chaotic systems with known and unknown parameters. Optik 127(13):5506–5514

    Article  Google Scholar 

  17. Yassen MT (2005) Chaos synchronization between two different chaotic systems using active control. Chaos Solitons Fractals 23(1):131–140

    Article  MATH  Google Scholar 

  18. Yang T, Chua LO (1998) Control of chaos using sampled data feedback control. Int J Bifurc Chaos 8(12):215–219

    Article  MATH  Google Scholar 

  19. Yu Y, Zhang S (2003) Controlling uncertain Lu system using backstepping design. Chaos Solitons Fractals 15(5):897–902

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhang H, Huang W, Wang Z, Chai T (2006) Adaptive synchronization between two different chaotic system. Phys Lett A 350(5–6):363–366

    Article  MATH  Google Scholar 

  21. Liu YJ, Wang ZF (2009) Adaptive fuzzy controller design of nonlinear systems with unknown gain sign. Nonlinear Dyn 58(4):687–695

    Article  MATH  Google Scholar 

  22. Chen D, Zhang R, Ma X, Liu S (2012) Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic system via a sliding mode control scheme. Nonlinear Dyn 69(1–2):35–55

    Article  MathSciNet  MATH  Google Scholar 

  23. Feng G, Cao J (2013) Master-slave synchronization of chaotic systems with modified impulsive controller. Adv Diff Equ 2013:24

  24. Liao XX, Chen GR (2003) Chaos synchronization of general Lur’e systems via time-delay feedback control. Int J Bifurc Chaos 13(1):207–213

  25. Ucar A, Lonngren KE, Bai EW (2008) Multi-switching synchronization of chaotic systems with active controllers. Chaos Solitons Fractals 38(1):254–262

    Article  Google Scholar 

  26. Wang XY, Sun P (2011) Multi-switching synchronization of chaotic system with adaptive controllers and unknown parameters. Nonlinear Dyn 63(4):599–609

    Article  MathSciNet  Google Scholar 

  27. Ajayi AA, Ojo SK, Vincent UE, Njah NA (2014) Multiswitching synchronization of a driven hyperchaotic circuit using active backstepping. J Nonlinear Dyn. doi:10.1155/2014/918586

    Google Scholar 

  28. Vincent UE, Saseyi AO, McClintock PVE (2015) Multi-switching combination synchronization of chaotic systems. Nonlinear Dyn 80(1):845–854

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhu F (2009) Observer-based synchronization of uncertain chaotic system and its application to secure communications. Chaos Soliton Fractals 40(5):2384–2391

    Article  MATH  Google Scholar 

  30. Yeh JP, Wu KL (2008) A simple method to synchronize chaotic systems and its application to secure communications. Math Comput Model 47(9–10):894–902

    Article  MathSciNet  MATH  Google Scholar 

  31. Xu X (2011) Generalized function projective synchronization of chaotic systems for secure communication. EURASIP J Adv Signal Process 2011:14–25

    Article  Google Scholar 

  32. Li Z, Xu D (2004) A secure communication scheme using projective chaos synchronization. Chaos Solitons Fractals 22(2):477–481

    Article  MATH  Google Scholar 

  33. Runzi L, Yinglan W, Shucheng D (2011) Combination synchronization of three classic chaotic systems using active beckstepping design. Chaos 21(4):043114

    Article  MATH  Google Scholar 

  34. Tigan G, Opris D (2008) Analysis of a 3-D chaotic system. Chaos Solitons Fractals 36(5):1315–1319

    Article  MathSciNet  MATH  Google Scholar 

  35. Liu C, Liu T, Liu L, Liu K (2004) A new chaotic attractor. Chaos Solitons Fractals 22(5):1031–1038

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, Delhi, 110025, India

    Ayub Khan

  2. Department of Mathematics, Shivaji College, Delhi, 110027, India

    Mridula Budhraja

  3. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Aysha Ibraheem

Authors
  1. Ayub Khan
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  2. Mridula Budhraja
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  3. Aysha Ibraheem
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Correspondence to Aysha Ibraheem.

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Khan, A., Budhraja, M. & Ibraheem, A. Multi-switching synchronization between T system and Liu system. Int. J. Dynam. Control 6, 609–620 (2018). https://doi.org/10.1007/s40435-017-0319-5

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  • DOI: https://doi.org/10.1007/s40435-017-0319-5

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