×

zbMATH — the first resource for mathematics

Hybrid projective synchronization in a chaotic complex nonlinear system. (English) Zbl 1151.93017
Summary: Hybrid Projective Synchronization (HPS), in which the different state variables can synchronize up to different scaling factors, is numerically observed in coupled partially linear chaotic complex nonlinear systems without adding any control term in the present paper. The scaling factors of HPS are hardly predictable. Linear feedback control method is thus adopted to control them onto any desired values based on Lyapunov stability theory. Moreover, numerical simulations are given to illustrate and verify the analytical results.

MSC:
93B52 Feedback control
93C10 Nonlinear systems in control theory
34C28 Complex behavior and chaotic systems of ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Elabbasy, E.M.; Agiza, H.N.; EI-Dessoky, M.M., Adaptive synchronization for four-scroll attractor with fully unknown parameters, Phys. lett. A, 349, 187-191, (2006)
[2] Hoang, T.M.; Nakagawa, M., Projective-lag synchronization of coupled multidelay feedback systems, J. phys. jpn., 75, 094801, (2006)
[3] Hu, M.F.; Xu, Z.Y.; Zhang, R.; Hu, A.H., Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems, Phys. lett. A, 361, 231-237, (2007) · Zbl 1170.93365
[4] Hu, M.F.; Xu, Z.Y.; Zhang, R.; Hu, A.H., Adaptive full state hybrid projective synchronization of chaotic systems with the same and different order, Phys. lett. A, 365, 315-327, (2007)
[5] Hung, Y.C.; Hwang, C.C.; Liao, T.L.; Yan, J.J., Generalized projective synchronization of chaotic systems with unknown dead-zone input: observer-based approach, Chaos, 16, 033125, (2006) · Zbl 1146.93368
[6] Hung, Y.C.; Hwang, C.C.; Liao, T.L.; Yan, J.J., Projective synchronization of synchronization of chua’s chaotic systems with dead-zone in the control input, Math. comput. simul., (2007)
[7] Li, C.G., Projective synchronization in fractional order chaotic systems and its control, Prog. theor. phys., 115, 661-666, (2006)
[8] Li, G.H.; Zhou, S.P.; Yang, K., Generalized projective synchronization between two different chaotic systems using active backstepping control, Phys. lett. A, 355, 326-330, (2006)
[9] Li, C.P.; Yan, J.P., Generalized projective synchronization of chaos: the cascade synchronization approach, Chaos solit. fract., 30, 140-146, (2006) · Zbl 1144.37370
[10] Liu, J.; Chen, S.H.; Lu, J.A., Projective synchronization in a unified chaotic system and its control, Acta phys. sin., 52, 1595-1599, (2003)
[11] Liu, W.B.; Chen, G.R., A new chaotic system and its generation, Int. J. bifurcat. chaos, 13, 261-267, (2003) · Zbl 1078.37504
[12] Mahmoud, G.M.; Aly, S.A.; Al-Kashif, M.A., Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system, Nonlinear dyn., (2007) · Zbl 1115.37035
[13] Mainieri, R.; Rehacek, J., Projective synchronization in three-dimensional chaotic systems, Phys. rev. lett., 82, 3042-3045, (1999)
[14] Park, J.H., Adaptive controller design for modified projective synchronization of genesio – tesi chaotic system with uncertain parameters, Chaos solit. fract., 30, 140-146, (2006)
[15] Perora, L.M.; Carroll, T.L., Synchronization in chaotic systems, Phys. rev. lett., 64, 821-825, (1990)
[16] Sun, J.T., Impulsive control of a new chaotic system, Math. comput. simul., 64, 669-677, (2004) · Zbl 1076.65119
[17] Xu, D., Control of projective synchronization in chaotic systems, Phys. rev. E, 63, 027201, (2001)
[18] Xu, D.; Chee, C.Y., Controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension, Phys. rev. E, 66, 046218, (2002)
[19] Xu, D.; Li, Z., Controlled projective synchronization in nonpartially-linear chaotic systems, Int. J. bifurcat. chaos, 12, 1395-1402, (2002)
[20] Xu, D.; Li, Z.; Bishop, R., Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems, Chaos, 11, 439-442, (2001) · Zbl 0996.37075
[21] Xu, D.; Ong, W.L.; Li, Z., Criteria for the occurrence of projective synchronization in chaotic systems of arbitrary dimension, Phys. lett. A, 305, 167-172, (2002) · Zbl 1001.37026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.