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The Generalized Synchronization of Bidirectionally Coupled Qi–Chen Systems via Linear Transformation

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Abstract

In this communication, we have discussed the theory of generalized synchronization of two bidirectionally coupled chaotic systems through linear transformation and have got a transformation matrix in general form. Also we have seen that for a special case the generalized synchronization becomes projective synchronization. We have applied this theory in two bidirectionally coupled Qi and Chen chaotic systems and discussed different cases for different forms of the transformation matrix. Finally numerical simulation results are presented and discussed to verify our claim.

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References

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

    Article  ADS  MATH  MathSciNet  Google Scholar 

  2. Li YN, Chen L, Cai ZS, Zhao XZ (2004) Experimental study on chaos synchronization in the Belousov-Zhabotinski chemical system. Chaos Solitons Fractals 22:767–771

    Article  ADS  MATH  Google Scholar 

  3. Ims RA, Andreassen HP (2000) Spatial synchronization of vole population dynamics by predator birds. Nature 408:194–196

    Article  ADS  Google Scholar 

  4. Carron N, Hahs DW (1997) A new approach to communication using chaotic signals. IEEE Trans Circuits Syst 408:373–382

    Article  Google Scholar 

  5. Ho MC, Hung YC (2002) System of two different systems by using generalized active control. Phys Lett A 301:424–428

    Article  ADS  MATH  MathSciNet  Google Scholar 

  6. Chen Lu (2005) Synchronization of an uncertain unified chaotic system via adaptive control. Chaos Solitons Fractals 23:1319–1325

    Article  Google Scholar 

  7. Yang T, Yang LB, Yang CM (1997) Impulsive control of Lorenz system. Physica D 110:18–24

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Yongguang Y, Suochun Z (2003) Controlling uncertain Lu system using back-stepping design. Chaos Solitons Fractal 15:897–902

    Article  ADS  MATH  Google Scholar 

  9. Yang T, Chua LO (1999) Generalized synchronization of chaos via linear transformations. Int J Bifurcat Chaos 9:215–219

    Article  MATH  MathSciNet  Google Scholar 

  10. Islam N, Karmokar P (2012) Generalized synchronization of finance chaotic system via linear transformation. Glob J Dyn Syst Appl 2:1–7

    Google Scholar 

  11. Khan MA, Mondal AK (2009) Generalized chaos synchronization of coupled Rossler systems. Bull Cal Math Soc 101:197–204

    MATH  Google Scholar 

  12. Khan MA, Poria S (2012) Generalized synchronization of bidirectionally coupled chaotic systems. Int J Appl Math Res 1(30):303–313

    Google Scholar 

  13. Ronnie M, Jan R (1999) Projective synchronization in three dimensional chaotic systems. Phys Rev Lett 82:3042–3045

    Article  Google Scholar 

  14. Khan MA, Poria S (2012) Projective synchronization of bidirectionally coupled chaotic systems via linear transformation. Int J Appl Math Res 1(4):541–548

    Google Scholar 

  15. Xu D, Chee C, Li C (2004) A necessary condition of projective synchronization in discrete-time systems of arbitrary dimensions. Chaos Solitons Fractals 22:175–180

    Article  ADS  MATH  MathSciNet  Google Scholar 

  16. Rulkov NF, Suschik MM, Tsimring LS (1995) Generalized of chaos in directionally coupled chaotic systems. Phys Rev E 51:980–994

    Article  ADS  Google Scholar 

  17. Harmov AE, Koronovskii AA, Moskalenko OI (2005) Generalized synchronization onset. Europhys Lett 72:901–907

    Article  ADS  MathSciNet  Google Scholar 

  18. Yang T, Chua LO (1999) Generalized synchronization of chaos via linear transformations. Int J Bifurcat Chaos 9:215–219

    Article  MATH  MathSciNet  Google Scholar 

  19. Poria S (2007) The linear generalized chaos synchronization and predictability. Int J Appl Mech Eng 12:879–885

    Google Scholar 

  20. Pal S, Sahoo B, Poria S (2013) Generalized lag synchronization of delay coupled chaotic systems via linear transformations. Phys Scr 87:045011

    Article  ADS  Google Scholar 

  21. Qi G, Chen G, Du S, Chen Z, Yuan Z (2005) Analysis of a new chaotic system. Phys A 352:295–308

    Article  Google Scholar 

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Authors and Affiliations

  1. Kolkata, India

    Pintu Karmokar & Nurul Islam

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  1. Pintu Karmokar
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  2. Nurul Islam
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Correspondence to Pintu Karmokar.

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Karmokar, P., Islam, N. The Generalized Synchronization of Bidirectionally Coupled Qi–Chen Systems via Linear Transformation. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 85, 137–141 (2015). https://doi.org/10.1007/s40010-014-0174-0

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  • DOI: https://doi.org/10.1007/s40010-014-0174-0

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