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Projective synchronization of new hyperchaotic system with fully unknown parameters. (English) Zbl 1204.93101
Summary: Projective synchronization of new hyperchaotic Newton-Leipnik system with fully unknown parameters is investigated in this paper. Based on Lyapunov stability theory, a new adaptive controller with parameter update law is designed to projective synchronize between two hyperchaotic systems asymptotically and globally. Basic bifurcation analysis of the new system is investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. It is found that the new hyperchaotic system possesses two positive Lyapunov exponents within a wide range of parameters. Numerical simulations on the hyperchaotic Newton-Leipnik system are used to verify the theoretical results.
MSC:
93D21Adaptive or robust stabilization
34C28Complex behavior, chaotic systems (ODE)
37D45Strange attractors, chaotic dynamics
37N35Dynamical systems in control
References:
[1]Chaos, Special issue on chaos synchronization 7(4) (1997) edited by Ditto, W.L., Showalter, K.
[2]Chen, G., Dong, X.: From Chaos to Order. Methodologies, Perspectives and Applications. World Scientific, Singapore (1998)
[3]Gonzalez-Miranda, J.M.: Phys. Rev. E 57, 7321 (1998) · doi:10.1103/PhysRevE.57.7321
[4]Mainieri, R., Rehacek, J.: Phys. Rev. Lett. 82, 3042 (1999) · doi:10.1103/PhysRevLett.82.3042
[5]Xu, D., Ong, W.L., Li, Z.: Phys. Lett. A 305, 167 (2002) · Zbl 1001.37026 · doi:10.1016/S0375-9601(02)01445-7
[6]Ghosh, D.: Chaos 19, 013102 (2009) · doi:10.1063/1.3054711
[7]Li, G.-H.: Chaos Solitons Fractals 32, 1786 (2007) · Zbl 1134.37331 · doi:10.1016/j.chaos.2005.12.009
[8]Ghosh, D., Saha, P., Roy Chowdhury, A.: Commun. Nonlinear Sci. Numer. Simul. (2009). doi: 10.1016/j.cnsns.2009.06.019
[9]Ghosh, D.: Int. J. Nonlinear Sci. 7, 207 (2009)
[10]Rössler, O.E.: Phys. Lett. A 71, 155 (1979) · Zbl 0996.37502 · doi:10.1016/0375-9601(79)90150-6
[11]Matsumoto, T., Chua, L.O., Kobayashi, K.: IEEE Trans. Circuits Syst. 33, 1143 (1986) · doi:10.1109/TCS.1986.1085862
[12]Li, Y., Tang, W.K.S., Chen, G.: Int. J. Bifurc. Chaos 15, 3367 (2005) · doi:10.1142/S0218127405013988
[13]Li, Y., Tang, W.K.S., Chen, G.: Int. J. Circuit Theory Appl. 33, 235 (2005) · Zbl 1079.34032 · doi:10.1002/cta.318
[14]Chen, A., Lu, J., Lu, J., Yu, S.: Physica A 364, 103 (2006) · doi:10.1016/j.physa.2005.09.039
[15]Wang, F.-Q., Liu, C.-X.: Chin. Phys. 15, 963 (2006) · doi:10.1088/1009-1963/15/5/016
[16]Newton, R.B., Leipnik, T.A.: Phys. Lett. A 86, 63 (1981) · doi:10.1016/0375-9601(81)90165-1
[17]Richter, H.: Phys. Lett. A 300, 182 (2002) · Zbl 0997.37012 · doi:10.1016/S0375-9601(02)00183-4
[18]Wang, X., Tian, L.: Chaos Solitons Fractals 27, 31 (2006) · Zbl 1091.93031 · doi:10.1016/j.chaos.2005.04.009
[19]Chen, H.K., Lee, C.I.: Chaos Solitons Fractals 21, 957 (2004) · Zbl 1046.70005 · doi:10.1016/j.chaos.2003.12.034
[20]Ghosh, D., Saha, P., Roy Chowdhury, A.: Int. J. Mod. Phys. C 19, 169 (2008) · Zbl 1145.93037 · doi:10.1142/S0129183108012005
[21]Kaplan, J.L., York, Y.A.: Commun. Math. Phys. 67, 93 (1979) · Zbl 0443.76059 · doi:10.1007/BF01221359
[22]El-Dessoky, M.M.: Anti-synchronization in four scroll attractor with fully unknown parameters. In: Nonlinear Analysis: Real World Applications (2009). doi: 10.1016/j.nonrwa.2009.01.048
[23]Huang, J.: Nonlin. Anal. 69, 4174 (2008) · Zbl 1161.34338 · doi:10.1016/j.na.2007.10.045