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Use of Alpha-Beta Filter to Synchronization of the Chaotic Ikeda Systems of Fractional Order

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Theoretical Developments and Applications of Non-Integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 357))

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Abstract

The paper considers a problem of signal filtering used in synchronization of two fractional delay Ikeda systems, combined linearly by coupling. Synchronization used Alpha-Beta filter, which operates on predicting the next value, based on measured signal in a current point in time. Using numerical simulations effects of fractional order and coupling rate on synchronization, is investigated. Simulations are performed using Ninteger Fractional Control Toolbox for MatLab.

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References

  1. Ben, H.: Description of an Alpha-beta Filter in Cartesian Coordinates, by Cantrell. Naval Research Lab Washington DC, (1973)

    Google Scholar 

  2. Busłowicz, M., Makarewicz, A.: Analysis of chaotic dynamics of the Ikeda system of fractional order. Pomiary, Automatyka, Robotyka 2/2013 (2013)

    Google Scholar 

  3. Busłowicz, M., Makarewicz, A.: Synchronization of the Chaotic Ikeda Systems of Fractional order. In: Mitkowski, W., Kacprzyk, J., Baranowski, J. (eds.) Advances in the Theory and Applications of Non-integer Order Systems, LNEE, vol. 257, pp. 261–269. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Das, S.: Functional Fractional Calculus for System Identification and Controls. Springer, Berlin (2008)

    MATH  Google Scholar 

  5. Dzieliński, A., Sierociuk, D., Sarwas, G.: Some applications of fractional order calculus. Bull. Pol. Acad. Sci., Tech. Sci. 58, 583–592 (2010)

    Google Scholar 

  6. Ikeda, K.: Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt. Commun. 30, 257–261 (1979)

    Article  Google Scholar 

  7. Ikeda, K., Matsumoto, K.: Study of a high-dimensional chaotic attractor. J. Stat. Phys. 44, 955–983 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jun-Guo, L.: Chaotic dynamics of the fractional-order Ikeda delay system and its synchronization. Chin. Phys. 15, 301–305 (2006)

    Article  Google Scholar 

  9. Kaczorek, T.: Selected Problems of Fractional Systems Theory. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

  10. Larger, L., Goedgebuer, J.P., Udaltsov, V.: Ikeda-based nonlinear delayed dynamics for application to secure optical transmission systems using chaos. C. R. Physique 5, 669–681 (2004)

    Article  Google Scholar 

  11. Luo, R., Wang, Y.: Dual lag quasi-synchronization of a class of chaotic systems with parameter mismatch. J. Inf. Comput. Sci. 7, 190–199 (2012)

    MathSciNet  Google Scholar 

  12. Monje, C., Chen, Y., Vinagre, B., Xue, D., Feliu, V.: Fractional-order Systems and Controls. Springer, London (2010)

    Book  MATH  Google Scholar 

  13. Ostalczyk, P.: Epitome of the Fractional Calculus, Theory and its Applications in Automatics. Publishing Department of Technical University of Łódź, Łódź (2008) (in Polish)

    Google Scholar 

  14. Petras, I.: Fractional-order Nonlinear Systems Modeling, Analysis and Simulation. Higher Education Press Beijing and Springer, Berlin Heidelberg (2011)

    Book  MATH  Google Scholar 

  15. Penoyer, R.: The alpha-beta filter; C. Users J. 11(7), 73–86 (1993)

    Google Scholar 

  16. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  17. Sabatier, J., Agrawal, O.P., Machado, J.A.T. (eds.): Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering. Springer, London (2007)

    MATH  Google Scholar 

  18. Sheu, L.J., Chen, W.C., Chen, Y.C., Wenig, W.T.: A two-channel secure communication using fractional chaotic systems. World Acad. Sci. Eng. Technol. 65, 1057–1061 (2010)

    Google Scholar 

  19. Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press, Oxford (2003)

    MATH  Google Scholar 

  20. Valério, D., Ninteger v. 2.3—Fractional Control Toolbox for MatLab, User and Programmer Manual, Technical University of Lisbona, Lisbona (2005). http://web.ist.utl.pt/duarte.valerio/ninteger/ninteger.htm

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Correspondence to Adam Makarewicz .

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Makarewicz, A. (2016). Use of Alpha-Beta Filter to Synchronization of the Chaotic Ikeda Systems of Fractional Order. In: Domek, S., Dworak, P. (eds) Theoretical Developments and Applications of Non-Integer Order Systems. Lecture Notes in Electrical Engineering, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-319-23039-9_17

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  • DOI: https://doi.org/10.1007/978-3-319-23039-9_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23038-2

  • Online ISBN: 978-3-319-23039-9

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