Synchronization Between Two Chaotic Systems: Numerical and Circuit Simulation
In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations for a specific chaotic system is conducted.
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[1] L.M. Pecora, T.L. Carroll, Phys, Rev, Lett. 64 (1990) 821-824.
[2] J.H. Park, Chaos Solitons Fractals 34 (2007) 1154.
[3] J.H. Park, O.M. Kwon, Chaos Solitons Fractals 23 (2005) 445.
[4] J. Lu, X. Wu, J. L¨u, Phys Lett A 305 (2002) 365.
[5] J. L¨u, T. Zhou, S. Zhang, Chaos Solitons Fractals 14 (2002) 529.
[6] J. L¨u, X. Yu, G. Chen, Physica A 334 (2004) 281.
[7] M.T. Yassen, Physics Letters A 350 (2006) 36.
[8] J.H. Park, O.M. Kwon, Modern Physics Letters B 23 (2009) 35.
[9] X. Wu, J. Lu, Chaos Solitons Fractals 18 (2003) 721.
[10] D. Li, J.A. Lu, X. Wu, Chaos Solitons Fractals 23 (2005) 79.
[11] U.E. Vincent, Phys Lett A 343 (2005) 133.
[12] J.H. Park, Chaos Solitons Fractals 27 (2006) 549.
[13] J.H. Park, Chaos Solitons Fractals 27 (2006) 357.
[14] M.G. Rosenblum, A.S. Pikovsky, J, Kurths, Phys. Rev. Lett 76 (1996)
1804.
[15] M.G. Rosenblum, A.S. Pikovsky, J, Kurths, Phys. Rev. Lett 78 (1997)
4193.
[16] S. Boccaletti, D.L. Valladares, Phys. Rev. E 62 (2000) 7497.
[17] A.E. Hramov, A.A. Koronovsii, Chaos 14 (2004) 603.
[18] A.E. Hramov, A.A. Koronovsii, Europhys. Lett. 72 (6) (2005) 901.
[19] R. Mainieri, J. Rehacek, Phys. Rev. Lett. 82 (1999) 304.
[20] J.H. Park, Chaos, Solitons Fractals, 34 (2007) 1154.
[21] J.H. Park, D.H. Ji, S.C. Won, and S.M. Lee, Modern Physics Letters B
23 (2009) 1157.
[22] J.H. Park, Chaos Solitons Fractals 25 (2005) 333.
[23] Y. Chen, H. An, Z. Li, Appl. Math. Comput. 197 (2008) 96.
[24] L. Runzi, Phys Lett A 372 (2008) 3667.
[25] K.M.Cuomo, A.V.Oppenheim, S.H.Strogatz, IEEE Trans Cir Syst-II 40
(1993) 626-633.
[26] T. Gao, G. Chen, Z. Chen, S. Cang, Phys Lett A 361 (2007) 78-86.
[27] K.M.Cuomo, A.V.Oppenheim, phys rev lett 71 (1993) 65-68.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54153", author = "J. H. Park and T. H. Lee and S. M. Lee and H. Y. Jung", title = "Synchronization Between Two Chaotic Systems: Numerical and Circuit Simulation", abstract = "In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations for a specific chaotic system is conducted.
", keywords = "Chaotic systems, synchronization, Lyapunov method, simulation.", volume = "4", number = "4", pages = "468-4", }