Abstract
The paper considers the modified Pandey-Baghel-Singh system of fractional order. Chaotic behavior of the system is analyzed and the problem of synchronization of two modified Pandey-Baghel-Singh systems via master-slave configuration with linear coupling is considered. A simple sufficient condition for synchronization using the Lyapunov and Gershgorin stability theory is proposed. The considerations are illustrated by numerical simulations.
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References
Busłowicz, M.: Stability of State-Space Models of Linear Continuous-time Fractional Order Systems. Acta Mechanica et Automatica 5, 15–22 (2011)
Busłowicz, M., Makarewicz, A.: Chaos Synchronization of the Modified Van der Pol-Duffing Oscillator of Fractional Order. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds.) Recent Advances in Automation, Robotics and Measuring Techniques. AISC, vol. 267, pp. 33–44. Springer, Heidelberg (2014)
Deleanu, D.: On a Sufficient Criterion for Global Synchronization in Chaotic Systems. In: Kanarachos, A. (ed.) Recent Advances in Telecommunications, Signals and Systems, pp. 95–100. WSEAS Press (2013)
Dibakar, G.A., Chowdhury, R., Saha, P.: On the Various Kinds of Synchronization in Delayed Duffing-Van der Pol System. Commun. Nonlinear Sci. Numer. Simulat. 13, 790–803 (2008)
Gantmacher, F.R.: The Theory of Matrices. Nauka, Moscow (1966) (in Russian)
He, G.T., Luo, M.: Dynamic Behavior of Fractional Order Duffing Chaotic System and its Synchronization via Singly Active Control. Appl. Math. Mech. 33(5), 567–582 (2012)
Jiang, G.-P., Tang, W.K.-S., Chen, G.: A Simple Global Synchronization criterion for Coupled Chaotic Systems. Chaos Solitons and Fractals 15, 925–935 (2003)
Kaczorek, T.: Selected Problems of Fractional Systems Theory. LNCIS, vol. 411. Springer, Berlin (2011)
Kenfack, G., Tiedeu, A.: Secured Transmission of ECG Signals: Numerical and Electronic Simulations. Journal of Signal and Information Processing 4, 158–169 (2013)
Kimiaeifar, A., Saidi, A.R., Sohouli, A.R., Ganji, D.D.: Analysis of Modified Van der Pol’s Oscillator Using He’s Parameter-Expanding Methods. Current Applied Physics 10, 279–283 (2010)
Mahmoud, G.M., Aly, S.A., Farghaly, A.A.: On Chaos Synchronization of a Complex Two Coupled Dynamos System. Chaos, Solitons and Fractals 33, 178–187 (2007)
Matouk, A.E.: Chaos, Feedback Control and Synchronization of a Fractional-Order Modified Autonomous Van der Pol–Duffing Circuit. Commun. Nonlinear Sci. Numer. Simulat. 16, 975–986 (2011)
Monje, C., Chen, Y., Vinagre, B., Xue, D., Feliu, V.: Fractional-Order Systems and Controls. Springer, London (2010)
Menacer, T., Hamri, N.: Synchronization of Different Chaotic Fractional-Order Systems via Approached Auxiliary System the Modified Chua Oscillator and the Modified Van der Pol-Duffing Oscillator. Electronic Journal of Theoretical Physics, EJTP 8(25), 253–266 (2011)
Ostalczyk, P.: Epitome of the Fractional Calculus, Theory and its Applications in Automatics. Publishing Department of Technical University of Łódź, Łódź (2008) (in Polish)
Pandey, A., Baghel, R.K., Singh, R.P.: Analysis and Circuit Realization of a New Autonomous Chaotic System. International Journal of Electronics and Communication Engineering 5(4), 487–495 (2012)
Petras, I.: Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation. Higher Education Press, Beijing, 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)
Suchorsky, M.K., Rand, R.H.: A Pair of Van der Pol Oscillators Coupled by Fractional Derivatives. Nonlinear Dyn. 69, 313–324 (2012)
Wang, Y., Yin, X., Liu, Y.: Control Chaos in System with Fractional Order. Journal of Modern Physics 3, 496–501 (2012)
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
Varga, R.S.: Gershgorin and His Circles. Springer, Berlin (2004)
Vincent, U.E., Odunaike, R.K., Laoye, J.A., Gbindinninuola, A.A.: Adaptive Backstepping Control and Synchronization of a Modified and Chaotic Van der Pol-Duffing Oscillator. J. Control Theory Appl. 9(2), 273–277 (2011)
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Busłowicz, M., Ruszewski, A., Makarewicz, A. (2015). Synchronization of the Chaotic Pandey-Baghel-Singh Systems of Fractional Order. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Progress in Automation, Robotics and Measuring Techniques. ICA 2015. Advances in Intelligent Systems and Computing, vol 350. Springer, Cham. https://doi.org/10.1007/978-3-319-15796-2_1
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DOI: https://doi.org/10.1007/978-3-319-15796-2_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15795-5
Online ISBN: 978-3-319-15796-2
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