Abstract
The paper considers the problem of synchronization of two fractional Ikeda delay systems via master/slave configuration with linear coupling. Using numerical simulations effects of fractional order and the coupling rate on synchronization is investigated. Simulations are performed using Ninteger Fractional Control Toolbox for MatLab.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Das, S.: Functional Fractional Calculus for System Identification and Controls. Springer, Berlin (2008)
Busłowicz, M.: Analysis of the Lorenz system of fractional order. Pomiary, Automatyka, Robotyka 2, 303–306 (2012) (in Polish)
Busłowicz, M., Makarewicz, A.: Analysis of chaotic dynamics of the Ikeda system of fractional order. Pomiary, Automatyka, Robotyka 2 (2013)
Chen, M., Kurths, J.: Synchronization of time-delayed systems. Physical Review E 76, 036212 (2007)
Dzieliński, A., Sierociuk, D., Sarwas, G.: Some applications of fractional order calculus. Bull. Pol. Acad. Sci., Tech. Sci. 58, 583–592 (2010)
Ikeda, K.: Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt. Commun. 30, 257–261 (1979)
Ikeda, K., Matsumoto, K.: Study of a high-dimensional chaotic attractor. Journal of Statistical Physics 44, 955–983 (1986)
Jun-Guo, L.: Chaotic dynamics of the fractional-order Ikeda delay system and its synchronization. Chinese Physics 15, 301–305 (2006)
Kaczorek, T.: Selected Problems of Fractional Systems Theory. Springer, Berlin (2011)
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)
Luo, R., Wang, Y.: Dual lag quasi-synchronization of a class of chaotic systems with parameter mismatch. Journal of Information and Computing Science 7, 190–199 (2012)
Monje, C., Chen, Y., Vinagre, B., Xue, D., Feliu, V.: Fractional-order Systems and Controls. Springer, London (2010)
Ostalczyk, P.: Epitome of the Fractional Calculus, Theory and its Applications in Automatics. Publishing Department of Technical University of Łódź, Łódź (2008) (in Polish)
Petras I.: Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation. Higher Education Press, Beijing and Springer, Heidelberg (2011)
Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
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)
Sheu, L.J., Chen, W.C., Chen, Y.C., Wenig, W.T.: A two-channel secure communication using fractional chaotic systems. World Academy of Science, Engineering and Technology 65, 1057–1061 (2010)
Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press, Oxford (2003)
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
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Busłowicz, M., Makarewicz, A. (2013). 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. Lecture Notes in Electrical Engineering, vol 257. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00933-9_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-00933-9_24
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00932-2
Online ISBN: 978-3-319-00933-9
eBook Packages: EngineeringEngineering (R0)