| Title:
|
Switched modified function projective synchronization between two complex nonlinear hyperchaotic systems based on adaptive control and parameter identification (English) |
| Author:
|
Zhou, Xiaobing |
| Author:
|
Jiang, Murong |
| Author:
|
Huang, Yaqun |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
632-642 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper investigates adaptive switched modified function projective synchronization between two complex nonlinear hyperchaotic systems with unknown parameters. Based on adaptive control and parameter identification, corresponding adaptive controllers with appropriate parameter update laws are constructed to achieve switched modified function projective synchronization between two different complex nonlinear hyperchaotic systems and to estimate the unknown system parameters. A numerical simulation is presented to demonstrate the validity and feasibility of the proposed controllers and update laws. (English) |
| Keyword:
|
modified function projective synchronization |
| Keyword:
|
switched state |
| Keyword:
|
hyperchaotic system |
| Keyword:
|
complex variable |
| Keyword:
|
adaptive control |
| MSC:
|
34C28 |
| MSC:
|
34D06 |
| MSC:
|
34H10 |
| idZBL:
|
Zbl 06386431 |
| idMR:
|
MR3275089 |
| DOI:
|
10.14736/kyb-2014-4-0632 |
| . |
| Date available:
|
2014-11-06T15:12:10Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143988 |
| . |
| Reference:
|
[1] Bhowmick, S. K., Pal, P., Roy, P. K., Dana, S. K.: Lag synchronization and scaling of chaotic attractor in coupled system..Chaos 22 (2012), 023151. 10.1063/1.4731263 |
| Reference:
|
[2] Chen, Y., Li, X.: Function projective synchronization between two identical chaotic systems..Int. J. Mod. Phys. C 18 (2007), 883-888. 10.1142/S0129183107010607 |
| Reference:
|
[3] Chen, Y., Lü, J., Yu, X., Lin, Z.: Consensus of discrete-time second-order multiagent systems based on infinite products of general stochastic matrices..SIAM J. Control Optim. 51 (2013), 3274-3301. Zbl 1275.93005, MR 3090151, 10.1137/110850116 |
| Reference:
|
[4] Chen, Y., Lü, J., Lin, Z.: Consensus of discrete-time multi-agent systems with transmission nonlinearity..Automatica 49 (2013), 1768-1775. MR 3049226, 10.1016/j.automatica.2013.02.021 |
| Reference:
|
[5] Chen, Y., Lü, J., Yu, X., Hill, D.: Multi-agent systems with dynamical topologies: Consensus and applications..IEEE Circuits Syst. Magazine 13 (2013), 21-34. 10.1109/MCAS.2013.2271443 |
| Reference:
|
[6] Du, H. Y., Zeng, Q. S., Wang, C. H.: Modified function projective synchronization of chaotic system..Chaos Solitons Fractals 42 (2009), 2399-2404. Zbl 1198.93011, 10.1016/j.chaos.2009.03.120 |
| Reference:
|
[7] Elabbasy, E. M., El-Dessoky, M. M.: Adaptive feedback control for the projective synchronization of the Lü dynamical system and its application to secure communication..Chin. J. Phys. 48 (2010), 863-872. |
| Reference:
|
[8] Feng, C. F., Zhang, Y., Sun, J. T., Qi, W., Wang, Y. H.: Generalized projective synchronization in time-delayed chaotic systems..Chaos, Solitons Fractals 38 (2008), 743-747. Zbl 1146.37318, 10.1016/j.chaos.2007.01.037 |
| Reference:
|
[9] Fowler, A. C., Gibbon, J. D., McGuinness, M. J.: The complex Lorenz equations..Physica D 4 (1982), 139-163. Zbl 1194.37039, MR 0653770, 10.1016/0167-2789(82)90057-4 |
| Reference:
|
[10] Grassi, G.: Generalized synchronization between different chaotic maps via dead-beat control..Chin. Phys. B 21 (2012), 050505. 10.1088/1674-1056/21/5/050505 |
| Reference:
|
[11] Lambert, J. D.: Numerical Methods for Ordinary Differential Systems: The Initial Value Problem..Wiley, New York 1991. Zbl 0745.65049, MR 1127425 |
| Reference:
|
[12] Li, G. H.: Modified projective synchronization of chaotic system..Chaos Solitons Fractals 32 (2007), 1786-1790. Zbl 1134.37331, MR 2299092, 10.1016/j.chaos.2005.12.009 |
| Reference:
|
[13] Liu, P., Liu, S. T., Li, X.: Adaptive modified function projective synchronization of general uncertain chaotic complex systems..Phys. Scr. 85 (2012), 035005. 10.1088/0031-8949/85/03/035005 |
| Reference:
|
[14] Lynnyk, V., Čelikovský, S.: On the anti-synchronization detection for the generalized lorenz system and its applications to secure encryption..Kybernetika 46 (2010) 1-18. Zbl 1190.93038, MR 2666891 |
| Reference:
|
[15] Ma, J., Li, F., Huang, L., Jin, W. Y.: Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system..Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 3770-3785. Zbl 1222.65136, 10.1016/j.cnsns.2010.12.030 |
| Reference:
|
[16] Ma, M. H., Zhang, H., Cai, J. P., al., et: Impulsive practical synchronization of n-dimensional nonautonomous systems with parameter mismatch..Kybernetika 49 (2013), 539-553. MR 3117913 |
| Reference:
|
[17] Mahmoud, G. M., Mahmoud, E. E.: Complete synchronization of chaotic complex nonlinear systems with uncertain parameters..Nonlinear Dyn. 62 (2010), 875-882. Zbl 1215.93114 |
| Reference:
|
[18] Mahmoud, G. M., Farghaly, A. A. M.: Chaos control of chaotic limit cycles of real and complex van der Pol oscillators..Chaos Solitons Fractals 21 (2004), 915-924. Zbl 1046.70014, MR 2042809, 10.1016/j.chaos.2003.12.039 |
| Reference:
|
[19] Mahmoud, G.M., Bountis, T., Mahmoud, E. E.: Active control and global synchronization of the complex Chen and Lü systems..Int. J. Bifur. Chaos 17 (2007), 4295-4308. Zbl 1146.93372, MR 2394229, 10.1142/S0218127407019962 |
| Reference:
|
[20] Mahmoud, G. M., Mahmoud, E. E., Ahmed, M. E.: A hyperchaotic complex Chen system and its dynamics..Int. J. Appl. Math. Stat. 12 (2007), 90-100. Zbl 1136.37327, MR 2374504 |
| Reference:
|
[21] Mahmoud, G. M., Ahmed, M. E., Mahmoud, E. E.: Analysis of hyperchaotic complex Lorenz systems..Int. J. Mod. Phys. C 19 (2008), 1477-1494. Zbl 1170.37311, 10.1142/S0129183108013151 |
| Reference:
|
[22] Mahmoud, G. M., Mahmoud, E. E., Ahmed, M. E.: On the hyperchaotic complex Lü system..Nonlinear Dyn. 58 (2009), 725-738. Zbl 1183.70053, MR 2563618 |
| Reference:
|
[23] Mahmoud, G. M., Al-Kashif, M. A., Farghaly, A. A.: Chaotic and hyperchaotic attractors of a complex nonlinear system..J. Phys. A: Math. Theor. 41 (2008), 055104. Zbl 1131.37036, MR 2433424, 10.1088/1751-8113/41/5/055104 |
| Reference:
|
[24] Mahmoud, G. M., Ahmed, M. E., Sabor, N.: On autonomous and nonautonomous modified hyperchaotic complex Lü systems..Int. J. Bifur. Chaos 21 (2011), 1913-1926. Zbl 1248.34053, MR 2835466, 10.1142/S0218127411029525 |
| Reference:
|
[25] Mahmoud, G. M., Ahmed, M. E.: A hyperchaotic complex system generating two-, three-, and four-scroll attractors..J. Vib. Control 18 (2012), 841-849. MR 2954367, 10.1177/1077546311405370 |
| Reference:
|
[26] Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensioned chaotic systems..Phys. Rev. Lett. 82 (1999), 3042-3045. 10.1103/PhysRevLett.82.3042 |
| Reference:
|
[27] Pecora, L. M., Carroll, T. L.: Synchronization in chaotic systems..Phys. Rev. Lett. 64 (1990), 821-824. Zbl 1098.37553, MR 1038263, 10.1103/PhysRevLett.64.821 |
| Reference:
|
[28] Shen, C., Yu, S., Lu, J., Chen, G.: A systematic methodology for constructing hyperchaotic systems with multiple positive Lyapunov exponents and circuit implementation..IEEE Trans. Circuits Syst. I 61 (2014), 854-864. 10.1109/TCSI.2013.2283994 |
| Reference:
|
[29] Sudheer, K. S., Sabir, M.: Switched modified function projective synchronization of hyperchaotic Qi system with uncertain parameters..Commun. Nonlinear Sci. Numer. Simul. 15 (2010), 4058-4064. 10.1016/j.cnsns.2010.01.014 |
| Reference:
|
[30] Wang, J. W., Chen, A. M.: Partial synchronization in coupled chemical chaotic oscillators..J. Comp. Appl. Math. 233 (2010), 1897-1904. Zbl 1194.34095, MR 2564025, 10.1016/j.cam.2009.09.026 |
| Reference:
|
[31] Wu, X. J., Wang, H., Lu, H. T.: Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication..Nonlinear Anal.: Real World Appl. 13 (2012), 1441-1450. Zbl 1239.94003, MR 2863970 |
| Reference:
|
[32] Yu, F., Wang, C. H., Wan, Q. Z., Hu, Y.: Complete switched modified function projective synchronization of a five-term chaotic system with uncertain parameters and disturbances..Pramana 80 (2013), 223-235. 10.1007/s12043-012-0481-4 |
| Reference:
|
[33] Zhou, P., Zhu, W.: Function projective synchronization for fractional-order chaotic systems..Nonlinear Anal.: Real World Appl. 12 (2011), 811-816. Zbl 1209.34065, MR 2736173 |
| . |
