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Hybrid dislocated control and general hybrid projective dislocated synchronization for the modified lü chaotic system. (English) Zbl 1198.93188
Summary: This paper introduces a modified Lü chaotic system, and some basic dynamical properties are studied. Based on these properties, we present hybrid dislocated control method for stabilizing chaos to unstable equilibrium and limit cycle. In addition, based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization (GHPDS) is proposed, which includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. The drive and response systems discussed in this paper can be strictly different dynamical systems (including different dimensional systems). As examples, the modified Lü chaotic system, Chen chaotic system and hyperchaotic Chen system are discussed. Numerical simulations are given to show the effectiveness of these methods. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
93D15Stabilization of systems by feedback
34H10Chaos control (ODE)
37D45Strange attractors, chaotic dynamics
37N35Dynamical systems in control
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References:
[1] Lorenz, E. N.: Deterministic nonperiodic flow, J atmos sci 20, 130-141 (1963)
[2] Fujisaka, H.; Yamada, T.: Stability theory of synchronized motion in coupled-oscillator systems, Progr theoret phys 69, 32-47 (1983) · Zbl 1171.70306 · doi:10.1143/PTP.69.32
[3] Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic system, Phys rev lett 64, 821-824 (1990) · Zbl 0938.37019
[4] Chen, G.; Dong, X.: From chaos to order: methodologies, perspectives, and applications, (1998) · Zbl 0908.93005
[5] Elabbssy, E. M.; Agiza, H. N.; El-Dessoky, M. M.: Adaptive synchronization of a hyperchaotic system with uncertain parameter, Chaos solit fract 30, 1133-1142 (2006) · Zbl 1142.37325 · doi:10.1016/j.chaos.2005.09.047
[6] Lü, J.; Lu, J.; Chen, Sh.: Chaotic time series analysis and its application, (2002)
[7] Chen, G.; Lü, J.: Dynamics of the Lorenz system family: analysis, control and synchronization, (2003)
[8] Li, Z.; Xu, D.: A secure communication scheme using projective chaos synchronization, Chaos soliton & fractals, No. 22, 477-481 (2004) · Zbl 1060.93530 · doi:10.1016/j.chaos.2004.02.019
[9] Lü, J.; Lu, J.: Controlling uncertain Lü system using linear feedback, Chaos soliton & fractals 17, 127-132 (2003) · Zbl 1039.37019 · doi:10.1016/S0960-0779(02)00456-3
[10] Huang, L. L.; Feng, R. P.; Wang, M.: Synchronization of chaotic systems via nonlinear control, Phys lett A 320, 271-275 (2004) · Zbl 1065.93028 · doi:10.1016/j.physleta.2003.11.027
[11] Luo, R.: Impulsive control and synchronization of a new chaotic system, Phys lett A 372, 648-653 (2008) · Zbl 1217.37033 · doi:10.1016/j.physleta.2007.08.010
[12] Wang, Y.; Guan, Zh.; Wang, H.: Feedback an adaptive control for the synchronization of Lu system via a single variable, Phys lett A 312, 34-40 (2003) · Zbl 1024.37053 · doi:10.1016/S0375-9601(03)00573-5
[13] L., G. Wen; Xu, D.: Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems, Chaos soliton & fractals 26, 71-77 (2005) · Zbl 1122.93311 · doi:10.1016/j.chaos.2004.09.117
[14] Wang, Y.; Guan, Z.: Generalized synchronization of continuous chaotic system, Chaos soliton & fractals 27, 97-101 (2006) · Zbl 1083.37515
[15] Li, G. H.: Generalized projective synchronization between Lorenz system and Lu’s system, Chaos soliton & fractals 32, 1454-1458 (2007) · Zbl 1129.37013 · doi:10.1016/j.chaos.2005.11.073
[16] Hu, M.; Xu, Zh.; Zhang, R.: Full state hybrid projective synchronization in continuous-time chaotic (hyperchaotic) systems, Commun nonlinear sci numer simul 13, 456-546 (2008) · Zbl 1123.37013 · doi:10.1016/j.cnsns.2006.05.003
[17] Lü, J.; Chen, G.: A new chaotic attractor coined, Int J bifur chaos 12, 659-661 (2002) · Zbl 1063.34510 · doi:10.1142/S0218127402004620
[18] Li, Y.; Tang, W. K. S.; Lu, G.: Generating hyperchaos via state feedback control, Int J bifur chaos 10, 3367-3375 (2005)