Anti-Synchronization of Tigan and Li Systems with Unknown Parameters via Adaptive Control

[1] Alligood, K.T., Sauer, T. & Yorke, J.A.,
Chaos: An Introduction to Dynamical
Systems, Springer, New York (1987).
[2] Lorenz, E., Deterministic nonperiodic flow, J.
Atmos. Sciences, 20, 130-141 (1963).
[3] Pecora, L.M. & Carroll, T.L., Synchronization
in chaotic systems, Phys. Rev. Letters, 64,
821-824 (1990).
[4] Lakshmanan, M. & Murali, K., Chaos in
Nonlinear Oscillators: Controlling and
Synchronization, World Scientific, Singapore
(1996).
[5] Han, S.K., Kerrer, C. & Kuramoto, Y.,
Dephasing and bursting in coupled neural
oscillators, Phys. Rev. Letters, 75, 3190-3193
(1995)
[6] Blasius, B., Huppert, A. & Stone, L.,
Complex dynamics and phase synchronization
in spatially extended ecological system,
Nature, 399, 354-359 (1999).
[7] Cuomo, K.M. & Oppenheim, A.V. Circuit
implementation of synchronized chaos with
applications to communications, Phys. Rev.
Letters, 71, 65-68 (1993).
[8] Li, Z., Li, K., Wen, C. & Soh, Y.C., A new
chaotic secure communication system, IEEE
Trans. Comm, 51 (8), 1306-1312 (2003).
[9] Ott, E., Grebogi, C. & Yorke, J.A., Controlling
chaos, Phys. Rev. Lett., 64, 1196-1199 (1990).
[10] Bai, E.W. & Longren, K.E., Synchronization
of two Lorenz systems using active control,
Chaos, Solit. Fractals, 8, 51-58 (1997).
[11] Ho, M.C. & Hung, Y.C., Synchronization of
two different chaotic systems using
generalized active control, Phys. Lett. A, 301,
424-428 (2002).
[12] Huang, L., Feng, R. & Wang, M.,
Synchronization of chaotic systems via
nonlinear control, Phys. Lett. A, 320, 271-275
(2005).
[13] Lei, Y., Xu, W., Shen, J. & Fang, T., Global
synchronization of two parametrically excited
systems using active control, Chaos Solit.
Fract., 28, 428-436 (2006).
[14] Chen, H.K., Global chaos synchronization of
new chaotic systems via nonlinear control,
Chaos Solit. Fract., 23, 1245-1251 (2005).
[15] Vincent, U.E., Synchronization of identical
and non-identical 4-D systems via active
control, Chaos Solit. Fract., 31, 119-129
(2007).
[16] Sundarapandian, V. & Karthikeyan, R., Global
chaos synchronization of hyperchaotic Liu and
hyperchaotic Chen systems by active nonlinear
control, CIIT Int. J. Digital Signal Processing,
3 (3), 134-139 (2011).
[17] Sundarapandian, V. & Karthikeyan, R., Global
chaos synchronization of Chen and Cai
systems by active nonlinear control, CIIT Int.
J. Digital Signal Processing, 3 (3), 140-144
(2011).
[18] Lu, J., Wu, X., Han, X. & Lü, J., Adaptive
feedback stabilization of a unified chaotic
system, Phys. Lett. A, 329, 327-333 (2004).
[19] Chen, S.H. & Lü, J., Synchronization of an
uncertian unified system via adaptive control,
Chaos Solit. Fract., 14, 643-647 (2002).
[20] Aghababa, M.P. & Aghababa, H.P., Adaptive
finite-time stabilization of uncertain nonautonomous
chaotic electromechanical
gyrostat systems with unknown parameters,
Mech. Research Commun., 38, 500-505
(2011).
[21] Aghababa, M.P., A novel adaptive finite-time
controller for synchronizing chaotic gyros with nonlinear inputs, Chinese Phys. B, 20, 090505
(2011).
[22] Aghababa, M.P. & Aghababa, H.P.,
Synchronization of nonlinear chaotic
electromechanical gyrostat systems with
undertainties, Nonlinear Dynamics,
doi:10.1007/s11071-011-0181-5 (2011).
[23] Aghababa, M.P. & Heydari, A., Chaos
synchronization between two different chaotic
systems with uncertainties, external
disturbances, unknown parameters and input
nonlinearities, Applied Math. Modelling,
doi:10.1016/j.apm.2011.09.023 (2011).
[24] Park, J.H. & Kwon, O.M., A novel criterion
for delayed feedback control of time-delay
chaotic systems, Chaos Solit. Fract., 17, 709-
716 (2003).
[25] Yu, Y.G. & Zhang, S.C., Adaptive
backstepping synchronization of uncertain
chaotic systems, Chaos Solit. Fract., 27, 1369-
1375 (2006).
[26] Idowu, B.A., Vincent, U.E. & Njah, A.N.,
Generalized adaptive backstepping
synchronization for non-identical
parametrically excited systems, Nonlinear
Analysis: Modelling and Control, 14 (2), 165-
176 (2009).
[27] Zhao, J. & Lü, J., Using sampled-data
feedback control and linear feedback
synchronization in a new hyperchaotic
system, Chaos Solit. Fract., 35, 376-382
(2006).
[28] Konishi, K., Hirai, M. & Kokame, H., Sliding
mode control for a class of chaotic systems,
Phys. Lett. A, 245, 511-517 (1998).
[29] Haeri, M. & Emazadeh, A.A.,
Synchronization of different chaotic systems
using active sliding mode control, Chaos
Solit. Fract., 119-129 (2007).
[30] Pourmahamood, M., Khanmohammadi, S. &
Alizadeh, G., Synchronization of two
different uncertain chaotic systems with
unknown parameters using a robust adaptive
sliding mode controller, Commun. Nonlinear
Sci. Numerical Simulat., 16, 2853-2868
(2011).
[31] Aghababa, M.P. & Khanmohammadi, S. &
Alizadeh, G., Finite-time synchronization of
two different chaotic systems with unknown
parameters via sliding mode technique, Appl.
Math. Model, 35, 3080-3091 (2011).
[32] Tigan, G. & Opris, D., Analysis of a 3D
chaotic system, Chaos Solit. Fract., 36, 1315-
1319 (2008).
[33] Li, X.F., Chlouverakis, K.E. & Xu, D.L.,
Nonlinear dynamics and circuit realization of a
new chaotic flow: A variant of Lorenz, Chen
and Lü, Nonlinear Analysis, 10, 2357-2368
(2009).
[34] Hahn, W., The Stability of Motion, Springer,
New York (1967).