Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
Adaptive Functional Projective Lag Synchronization of Lorenz System

Authors: Tae H. Lee, J.H. Park, S.M. Lee, H.Y. Jung

Abstract:

This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion is given for asymptotical stability of the null solution of an error dynamics. Finally, some numerical examples are provided to show the effectiveness of our results.

Keywords: Adaptive function projective synchronization, Chaotic system, Lag synchronization, Lyapunov method

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062892

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1267

References:


[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.