Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:B2L-D

Session:

Number:395

Synchronization without correlation

Miguel C. Soriano,  Guy Van der Sande,  Ingo Fischer,  Claudio R. Mirasso,  

pp.395-398

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.395

PDF download (643.8KB)

Summary:
In this work, we address two fundamental questions in the field of delay-coupled oscillators: Does the synchronization between coupled oscillators necessarily imply correlations? What can be inferred from the absence of correlations in networks of coupled nonlinear dynamical elements about their connectivity? We show that for a realistic configuration of delay-coupled dynamical elements negligible correlation or mutual information are observed, although the elements are synchronized and determine each others' behaviors completely. We employ for these results delay-coupled Mackey-Glass oscillators, presenting experimental results on the emergence of identically synchronized behavior between distant elements mediated via a signal with negligible correlations but synchronized in the generalized sense.

References:

[1] L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems”, Phys. Rev. Lett., vol. 64, pp. 821-824, 1990.

[2] L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals”, Phys. Rev. A, vol. 44, pp. 2374-2383, 1991.

[3] S. Sano, A. Uchida, S. Yoshimori, and R. Roy, “Dual synchronization of chaos in Mackey-Glass electronic circuits with time-delayed feedback”, Phys. Rev. E , vol. 75, pp. 016207(1)-(6), 2007.

[4] A. Wagemakers, J. M. Buldú and M. A. F. Sanjuán, “Experimental demonstration of bidirectional chaotic communication by means of isochronal synchronization”, Europ. Phys. Lett., vol. 81, pp. 40005(1-5), 2008.

[5] A. Namajunas, K. Pyragas, and A. Tamaševicius, “An electronic analog of the Mackey-Glass system”, Physics Letters A, vol. 201, pp. 42-46, 1995.

[6] G. Van der Sande, M.C. Soriano, I. Fischer, and C.R. Mirasso, “Dynamics, correlation scaling, and synchronization behavior in rings of delay-coupled oscillators”, Phys. Rev. E , vol. 77, pp. 055202(R)(1-4), 2008.

[7] M.C. Soriano, G. Van der Sande, I. Fischer, and C.R. Mirasso, “Synchronization in Simple Network Motifs with Negligible Correlation and Mutual Information Measures”, Phys. Rev. Lett., vol. 108, pp. 134101(1-5), 2012.

[8] Andrew M. Fraser and Harry L. Swinney, “Independent coordinates for strange attractors from mutual information”, Phys. Rev. A, vol. 33, pp. 1134-1140, 1986.

[9] H.D.I. Abarbanel, N.F. Rulkov, and M.M. Sushchik, “Generalized synchronization of chaos: The auxiliary system approach”, Phys. Rev. E vol. 53, pp. 4528-4535, 1996.