Hybrid phase synchronization between identical and nonidentical three-dimensional chaotic systems using the active control method

Nonlinear Dynamics

Volumn 73, Issue 4, 2013, Pages 2261-2272

  Das, S ^a   Srivastava, M ^a   Leung, A Y T ^b,c  

^a BANARAS HINDU UNIVERSITY   (India)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^c UNIVERSITY OF HUDDERSFIELD   (United Kingdom)

Author keywords

Active control method; Chaos; Hybrid synchronization; Phase synchronization; Rikitake system; Windmi system

Indexed keywords

ACTIVE CONTROL METHODS; HYBRID SYNCHRONIZATIONS; PHASE SYNCHRONIZATION; RIKITAKE SYSTEM; WINDMI SYSTEM;

CHAOS THEORY; CHAOTIC SYSTEMS; COMPUTER SIMULATION; CONTROL THEORY; RUNGE KUTTA METHODS;

SYNCHRONIZATION;

EID: 84882454634     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-0939-z     Document Type: Article

References (48)

1. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821-824 (1990)
2. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196-1199 (1990)
3. Chen, G., Dong, X.: From Chaos to Order: Methodologies, Perspectives and Applications. World Scientific, Singapore (1998)
4. Fuh, C.C., Tung, P.C.: Controlling chaos using differential geometric method. Phys. Rev. Lett. 75, 2952-2955 (1995)
5. Zhang, Y., Sun, J.: Chaotic synchronization and anti-synchronization based on suitable separation. Phys. Lett. A 330, 442-447 (2004)
6. Blasius, B., Huppert, A., Stone, L.: Complex dynamics and phase synchronization in spatially extended ecological system. Nature 399, 354-359 (1999)
7. Lakshmanan, M., Murali, K.: Chaos in Nonlinear Oscillators: Controlling and Synchronization. World Scientific, Singapore (1996)
8. Han, S.K., Kerrer, C., Kuramoto, Y.: D-phasing and bursting in coupled neural oscillators. Phys. Rev. Lett. 75, 3190-3193 (1995)
9. Cuomo, K.M., Oppenheim, A.V.: Circuit implementation of synchronized chaos with application to communication. Phys. Rev. Lett. 71, 65-68 (1993)
10. Kocarev, L., Parlitz, U.: General approach for chaotic synchronization with applications to communication. Phys. Rev. Lett. 74, 5028-5030 (1995)
11. Murali, K., Lakshmanan, M.: Secure communication using a compound signal using sampled-data feedback. Appl. Math. Mech. 11, 1309-1315 (2003)
12. Chen, S.H., Lu, J.: Parameters identification and synchronization of chaotic systems based upon adaptive control. Phys. Lett. A 299, 353-358 (2002)
13. Huang, L., Feng, R., Wang, M.: Synchronization of chaotic systems via nonlinear control. Phys. Lett. A 320, 271-275 (2004)
14. Park, J.H., Kwon, O.M.: A novel criterion for delayed feedback control of time-delay chaotic systems. Chaos Solitons Fractals 23, 495-501 (2005)
15. Zhu, Q., Cao, J.: Adaptive synchronization of chaotic Cohen-Crossberg neural networks with mixed time delays. Nonlinear Dyn. 61, 517-534 (2010)
16. Odibat, Z.M.: Adaptive feedback control and synchronization of non-identical chaotic fractional order systems. Nonlinear Dyn. 60, 479-487 (2010)
17. Ho, M.C., Hung, Y.C.: Synchronization of two different systems by using generalized active control. Phys. Lett. A 301, 424-429 (2002)
18. Yassen, M.T.: Chaos synchronization between two different chaotic systems using active control. Chaos Solitons Fractals 23, 131-140 (2005)
19. Wu, X., Lü, J.: Parameter identification and backstepping control of uncertain Lü system. Chaos Solitons Fractals 18, 721-729 (2003)
20. Yau, H.T.: Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos Solitons Fractals 22, 341-347 (2004)
21. Faieghi, M.R., Delavari, H.: Chaos in fractional-order Genesio-Tesi system and its synchronization. Commun. Nonlinear Sci. Numer. Simul. (2011). doi: 10.1016/j.cnsns.2011.05.038
22. Yang, S.S., Juan, C.K.: Generalized synchronization in chaotic systems. Chaos Solitons Fractals 9, 1703-1707 (1998)
23. Yang, X.S.: On the existence of generalized synchronization in unidirectional coupled systems. Appl. Math. Comput. 122, 71-79 (2000)
24. Yu, H.J., Liu, Y.Z.: Chaotic synchronization based on stability criterion of linear systems. Phys. Lett. A 314, 292-298 (2003)
25. Rosenblum, M.G., Pikovsky, A.S., Kurths, J.: From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 78, 4193-4196 (1997)
26. Taherion, S., Lai, Y.C.: Observability of lag synchronization of coupled chaotic oscillators. Phys. Rev. E 59, 6247-6250 (1999)
27. Park, E.H., Zaks, M.A., Kurths, J.: Phase synchronization in the forced Lorenz system. Phys. Rev. E 60, 6627-6638 (1999)
28. 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)
29. Erjaee, G.H., Momani, S.: Phase synchronization in fractional differential chaotic systems. Phys. Lett. A 372, 2350-2354 (2008)
30. Mahmoud, G.M., Mahmoud, E.E.: Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems. Nonlinear Dyn. 61, 141-152 (2010)
31. Wang, Z.-L., Shi, X.-R.: Anti-synchronization of Liu system and Lorenz system with known or unknown parameters. Nonlinear Dyn. 57, 425-430 (2009)
32. Li, G.H., Zhou, S.P.: An observer-based anti-synchronization. Chaos Solitons Fractals 29, 495-498 (2006)
33. Hu, J., Chen, S., Chen, L.: Adaptive control for anti-synchronization of Chua's chaotic system. Phys. Lett. A 339, 455-460 (2005)
34. Boccaletti, S., Valladares, D.L.: Characterization of intermittent lag synchronization. Phys. Rev. E 62, 7497-7500 (2000)
35. Hramov, A.E., Koronovskii, A.A.: An approach to chaotic synchronization. Chaos 14, 603-610 (2004)
36. Hramov, A.E., Koronovskii, A.A., Moskalenko, O.I.: Generalized synchronization onset. Europhys. Lett. 72, 901-907 (2005)
37. Ghosh, D., Bhattacharya, S.: Projective synchronization of new hyperchaotic system with fully unknown parameters. Nonlinear Dyn. 61, 11-21 (2010)
38. Li, G.-H.: Modified projective synchronization of chaotic system. Chaos Solitons Fractals 32, 1786-1790 (2007)
39. Runzi, L.: Adaptive function project synchronization of Rossler hyperchaotic system with uncertain parameters. Phys. Lett. A 372, 3667-3671 (2008)
40. Xie, Q., Chen, G.: Hybrid chaos synchronization and its application in information processing. Math. Comput. Model. 35, 145-163 (2002)
41. Barajas-Ramirez, J.-G., Chen, G., Shieh, L.S.: Hybrid chaos synchronization. Int. J. Bifurc. Chaos 13, 1197-1216 (2003)
42. Vaidyanathan, S.: Hybrid synchronization of Liu and Lu chaotic systems via adaptive control. Int. J. Adv. Inf. Technol. 1, 11-21 (2011)
43. Shi, X., Wang, Z.: The alternating between complete synchronization and hybrid synchronization of hyperchaotic Lorenz system with time delay. Nonlinear Dyn. (2012). doi: 10.1007/s11071-012-0339-9
44. Njah, A.N.: Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques. Nonlinear Dyn. 61, 1-9 (2010)
45. Yu, Y., Li, H.-X.: Adaptive hybrid projective synchronization of uncertain chaotic systems based on back stepping design. Nonlinear Anal., Real World Appl. 12, 388-393 (2011)
46. Wu, X.-J., Liu, J.-S., Chen, G.-R.: Chaos synchronization of Rikitake chaotic attractor using the passive control technique. Nonlinear Dyn. 53, 45-53 (2008)
47. Xin, B., Chen, T., Liu, Y.: Synchronization of chaotic fractional order Windmi systems via linear state error feedback control. Math. Probl. Eng. (2010). doi: 10.1155/2010/859685
48. Horton, W., Doxas, I.: A low-dimensional dynamical model for the solar wind driven geotailionosphere system. J. Geophys. Res. A 103, 4561-4572 (1998)