Hybrid robust modified function projective lag synchronization in two different dimensional chaotic systems

Nonlinear Dynamics

Volumn 73, Issue 1-2, 2013, Pages 245-257

  Luo, Chao ^a   Wang, Xingyuan ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Adaptive control; Hybrid system; Modified function projective lag synchronization (MFPLS); Robustness

Indexed keywords

ADAPTIVE CONTROL; ADAPTIVE CONTROLLERS; LYAPUNOV STABILITY THEORY; NONIDENTICAL CHAOTIC SYSTEMS; PARAMETER PERTURBATION; PROJECTIVE LAG SYNCHRONIZATIONS; SCALING FUNCTIONS; SYNCHRONIZATION SCHEME;

ADAPTIVE CONTROL SYSTEMS; CHAOTIC SYSTEMS; HYBRID SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS);

SYNCHRONIZATION;

EID: 84879781118     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-0781-3     Document Type: Article

References (30)

1. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821-824 (1990)
2. Shinbrot, T., Grebogi, C., Ott, E., Yorke, J.A.: Using small perturbations to control chaos. Nature 363(6), 411-417 (1993)
3. Liu, Y.J., Wang, W.: Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inf. Sci. 177(18), 3901-3917 (2007)
4. Shahverdiev, E.M., Sivaprakasam, S., Shore, K.A.: Lag synchronization in time-delayed systems. Phys. Lett. A 292(6), 320-324 (2002)
5. Liu, C.X., Liu, L., Liu, T., Li, P.: A new butterfly-shaped attractor of Lorenz-like system. Chaos Solitons Fractals 28, 1197-1203 (2006)
6. Liu, Y.J., Zheng, Y.Q.: Adaptive robust fuzzy control for a class of uncertain chaotic systems. Nonlinear Dyn. 57(3), 431-439 (2009)
7. Yang, X.S.: On the existence of generalized synchronizor in unidirectionally coupled systems. Appl. Math. Comput. 122(1), 71-79 (2001)
8. Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett. 82(15), 3042-3045 (1999)
9. Liu, Y.J., Chen, C.L.P., Wen, G.X., Tong, S.C.: Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans. Neural Netw. 22(7), 1162-1167 (2011)
10. Rosenblum, M.G., Pikovsky, A.S., Kurths, J.: From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 78(22), 4193-4196 (1997)
11. Liu, C.X., Liu, L., Liu, T.: A novel three-dimensional autonomous chaos system. Chaos Solitons Fractals 22, 1031-1038 (2004)
12. Wang, X.Y., Zhang, Y.L.: Modified projective synchronization of fractional-order hyperchaotic system with single driving variable. Chin. Phys. B 20(10), 100506 (2011)
13. Liu, Y.J., Wang, W., Tong, S.C., Liu, Y.S.: Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 40(1), 170-184 (2010)
14. Yu, X., Song, Y.: Chaos synchronization via controlling partial state of chaotic systems. Int. J. Bifurc. Chaos 11(6), 1737-1741 (2001)
15. Liu, L., Liu, C.X., Zhang, Y.B.: Experimental verification of a four-dimensional Chua's system and its fractional order chaotic attractors. Int. J. Bifurc. Chaos 19(8), 2473-2486 (2009)
16. Du, H., Zeng, Q., Wang, C.: Function projective synchronization of different chaotic systems with uncertain parameter. Phys. Lett. A 372, 5402-5410 (2008)
17. Wang, X.Y., Liu, R., Zhang, N.: Function projective synchronization of fractional-order hyperchaotic system based on open-plus-closed-looping. Commun. Theor. Phys. 55(4), 617-621 (2011)
18. Du, H., Zeng, Q., Lü, N.: A general method for modified function projective lag synchronization in chaotic systems. Phys. Lett. A 374(13-14), 1493-1496 (2010)
19. Sebastian, K.S., Sabir, M.: Adaptive modified function projective synchronization of multiple time-delayed chaotic Rössler system. Phys. Lett. A 375(8), 1176-1178 (2011)
20. Zheng, S., Dong, G.G., Bi, Q.S.: Adaptive modified function projective synchronization of hyperchaotic systems with unknown parameters. Commun. Nonlinear Sci. Numer. Simul. 15(11), 3547-3556 (2010)
21. Yu, Y.G., Li, H.X.: Adaptive generalized function projective synchronization of uncertain chaotic systems. Nonlinear Anal., Real World Appl. 11(4), 2456-2464 (2010)
22. Bazhenov, M., Huerta, R., Rabinovich, M.I., Sejnowski, T.: Cooperative behavior of a chain of synaptically coupled chaotic neurons. Physica D 116, 392-400 (1998)
23. Ho, M.C., Hung, Y., Liua, Z., Jiang, I.: Reduced-order synchronization of chaotic system with parameters unknown. Phys. Lett. A 348, 251-259 (2006)
24. Cai, N., Li, W.Q., Jing, Y.W.: Finite-time generalized synchronization of chaotic systems with different order. Nonlinear Dyn. 64(4), 385-393 (2011)
25. Wang, S., Yu, Y.G., Diao, M.: Hybrid projective synchronization of chaotic fractional order systems with different dimensions. Physica A 389, 4981-4988 (2010)
26. Li, S.Y., Ge, Z.M.: Generalized synchronization of chaotic systems with different orders by fuzzy logic constant controller. Expert Syst. Appl. 38(3), 2302-2310 (2011)
27. Rössler, O.E.: An equation for continuous chaos. Phys. Lett. 57(5), 397-398 (1976)
28. Hammami, S., Benrejeb, M., Feki, M.: Feedback control design for Rössler and Chen systems anti-synchronization. Phys. Lett. A 374(28), 2835-2840 (2010)
29. Sebastian, S.K., Sabir, M.: Adaptive modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system with uncertain parameters. Phys. Lett. A 373, 3743-3748 (2009)
30. Chen, A., Lu, J., Lü, J., Yu, S.: Generating hyperchaotic Lü attractor via state feedback control. Physica A 364, 103-110 (2006)