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Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters. (English) Zbl 1231.37020
Summary: This paper presents the adaptive anti-synchronization of a class of chaotic complex nonlinear systems described by a united mathematical expression with fully uncertain parameters. Based on Lyapunov stability theory, an adaptive control scheme and adaptive laws of parameters are developed to anti-synchronize two chaotic complex systems. The anti-synchronization of two identical complex Lorenz systems and two different complex Chen and Lü systems are taken as two examples to verify the feasibility and effectiveness of the presented scheme.

MSC:
37D45Strange attractors, chaotic dynamics
34H10Chaos control (ODE)
93C40Adaptive control systems
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References:
[1] Fowler, A. C.; Gibbon, J. D.; Mcguinness, M. J.: The complex Lorenz equations, Physica D 4, 139-163 (1982) · Zbl 1194.37039 · doi:10.1016/0167-2789(82)90057-4
[2] Mahmoud, G. M.; Bountis, T.; Mahmoud, E. E.: Active control and global synchronization for complex Chen and Lü systems, Internat. J. Bifur. chaos 17, 4295-4308 (2007) · Zbl 1146.93372 · doi:10.1142/S0218127407019962
[3] Mahmoud, G. M.; Mahmoud, E. E.; Ahmed, M. E.: On the hyperchaotic complex Lü system, Nonlinear dyn. 58, 725-738 (2009) · Zbl 1183.70053 · doi:10.1007/s11071-009-9513-0
[4] Mahmoud, G. M.; Aly, S. A.; Al-Kashif, M. A.: Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system, Nonlinear dyn. 51, 171-181 (2008) · Zbl 1170.70365 · doi:10.1007/s11071-007-9200-y
[5] Mahmoud, G. M.; Mahmoud, E. E.: Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems, Nonlinear dyn. 61, 141-152 (2010) · Zbl 1204.93096 · doi:10.1007/s11071-009-9637-2
[6] Mahmoud, G. M.; Mahmoud, E. E.: Complete synchronization of chaotic complex nonlinear systems with uncertain parameters, Nonlinear dyn. 62, 875-882 (2010) · Zbl 1215.93114 · doi:10.1007/s11071-010-9770-y
[7] Hu, J.; Chen, S.; Chen, L.: Adaptive control for anti-synchronization of Chua’s chaotic system, Phys. lett. A 339, 455-460 (2005) · Zbl 1145.93366 · doi:10.1016/j.physleta.2005.04.002
[8] Kim, C. M.; Rim, S.; Kye, W. H.; Ryu, J. W.; Park, Y. J.: Anti-synchronization of chaotic oscillators, Phys. lett. A 320, 39-46 (2003) · Zbl 1098.37521 · doi:10.1016/j.physleta.2003.10.051
[9] Zhang, Y.; Sun, J.: Chaotic synchronization and anti-synchronization based on suitable separation, Phys. lett. A 330, 442-447 (2004) · Zbl 1209.37039 · doi:10.1016/j.physleta.2004.08.023
[10] Ho, M. C.; Hung, Y. C.; Chou, C. H.: Phase and anti-phase synchronization of two chaotic systems by using active control, Phys. lett. A 296, 43-48 (2002) · Zbl 1098.37529 · doi:10.1016/S0375-9601(02)00074-9
[11] Li, G. H.; Zhou, S. P.: Anti-synchronization in different chaotic systems, Chaos solitons fractals 32, 516-520 (2007)
[12] Li, W.; Chen, X.; Shen, Z.: Anti-synchronization of two different chaotic systems, Physica A 387, 3747-3750 (2008)
[13] Al-Sawalha, M. M.; Noorani, M. S. M.: Adaptive anti-synchronization of two identical and different hyperchaotic systems with uncertain parameters, Commun. nonlinear sci. Numer. simul. 15, 1036-1047 (2010) · Zbl 1221.93123 · doi:10.1016/j.cnsns.2009.05.037
[14] Mahmoud, G. M.; Al-Kashif, M. A.; Aly, S. A.: Basic properties and chaotic synchronization of complex Lorenz system, Internat. J. Modern. phys. C 18, 253-265 (2007) · Zbl 1115.37035 · doi:10.1142/S0129183107010425