---

Journal of Applied Nonlinear Dynamics 3(3) (2014) 245--253 | DOI:10.5890/JAND.2014.09.004

Siddharth Arora$^{1}$; M.S. Santhanam$^{2}$

$^{1}$ Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6HD, U.K.

$^{2}$ Indian Institute of Science Education and Research, Sutarwadi Road, Pashan, Pune, 411021,India

Download Full Text PDF

 

Abstract

We apply the method of variable feedback to obtain complete synchronization in a coupled map lattice. The conditions under which such a synchronization is possible are obtained analytically. We show that synchronization is robust against noise and parameter mismatches. This method leads to synchronized state quite rapidly and we discuss its applications for near-real-time multi-channel communications.

References

1. [1]	Pecora, L.M. and Carroll, T.L. (1990), Synchronization in chaotic systems, Physical Review Letters, 64, 821-825.

2. [2]	Pikovsky, A., Rosenblum, M., and Kurths, J. (2001), Synchronization: A universal concept in nonlinear sciences, (Cambridge).

3. [3]	Boccaletti; S., Kurths, J., Osipov, G., Valladares, D.L., and Zhou, C.S. (2002), The synchronization of chaotic systems, Physics Reports, 366, 1-101.

4. [4]	Glass, L. (2001), Synchronization and rhythmic processes in physiology, Nature, 410, 277-284.

5. [5]	Quian Quiroga, R., Kraskov, A., Kreuz, T., and Grassberger, P. (2002), Performance of different synchronization measures in real data: A case study on electroencephalographic signals, Physical Review E, 65, 041903-14.

6. [6]	Theory and applications of coupled map lattices, edited by K. Kaneko (Wiley, New York, 1993).

7. [7]	Ahalpara, D.P., Arora, S., and Santhanam, M.S. (2009), Genetic programming based approach for synchronization with parameter mismatches in EEG, Lecture Notes in Computer Science, 5481, 13-24.

8. [8]

   Kocarev, L. and Parlitz, U. (1995), General approach for chaotic synchronization with applications to communication, Physical Review Letters, 74, 5028-5031; Jinlan, W., Guangzhi, C., Tuanfa, Q., Wansun, N. and Xuming, W. (1998), Synchronizing spatiotemporal chaos in coupled map lattices via active-passive decomposition, Physical Review E, 58, 3017-3021.

9. [9]	Sinha, S. (2002), Random coupling of chaotic maps leads to spatiotemporal synchronization, Physical Review E, 66, 016209-6.

10. [10]	Santhanam, M.S. and Arora, S. (2007), Zero delay synchronization of chaos in coupled map lattices, Physical Review E, 76, 026202-8.

11. [11]	Pyragas, K. (1992), Continuous control of chaos by self-controlling feedback, Physics Letters A, 170, 421-428.

12. [12]	Morgul, O. (1998), On the synchronization of logistic maps, Physics Letters A, 247, 391-396.

13. [13]	Ali, M.K. and Fang, J-Q. (1997), Synchronization of chaos and hyperchaos using linear and nonlinear feedback functions, Physical Review E, 55, 5285-5290.

14. [14]	Xiao, J.H., Hu, G., and Qu, Z. (1996), Synchronization of Spatiotemporal Chaos and Its Application to Multichannel Spread-Spectrum Communication, Physical Review Letters, 77, 4162-4165.

15. [15]	Argyris, A., Syvridis, D., Larger, L., Annovazzi-Lodi, V., Colet, P., Fischer, I., Garcia-Ojalvo, J., Mirasso, C.R., Pesquera, L., and Shore, K.A. (2005), Chaos-based communications at high bit rates using commercial fibre-optic links, Nature, 438, 343-346.

16. [16]	Moskalenko, O.I., Koronovskii, A.A., and Hramov, A.E. (2010), Generalized synchronization of chaos for secure communication: Remarkable stability to noise, Physics Letters A, 374, 2925-2931.

17. [17]	Kinzel, W., Englert, A., and Kanter, I. (2010), On chaos synchronization and secure communication, Philosophical Transactions of the Royal Society: A, 368, 379-389.

18. [18]	Li, P., Wu, J-G., Wu, Z-M., Lin, X-D., Deng, D., Liu, Y-R., and Xia, G-Q. (2011), Bidirectional chaos communication between two outer semiconductor lasers coupled mutually with a central semiconductor laser, Optics Express, 19, 23921-23931.

19. [19]	Kaneko, K. (1989), Spatiotemporal chaos in one- and two-dimensional coupled map lattices, Physica D, 37, 60-82.

20. [20]	Pikovsky, A.S., Rosenblum, M.G., Osipov, G.V., and Kurths, J. (1997), Phase synchronization of chaotic oscillators by external driving, Physica D: Nonlinear Phenenomena, 104, 219-238.

21. [21]	Shabunin, A., Demidov, V., Astakhov, V., and Anishchenko, V. (2002), Information theoretic approach to quantify complete and phase synchronization of chaos, Physical Review E, 65, 056215-5.