Phase transition in crowd synchrony of delay-coupled multilayer laser networks

doi:10.1364/OE.20.019683

Phase transition in crowd synchrony of delay-coupled multilayer laser networks

Elad Cohen, Michael Rosenbluh, and Ido Kanter »View Author Affiliations

Optics Express, Vol. 20, Issue 18, pp. 19683-19689 (2012)
http://dx.doi.org/10.1364/OE.20.019683

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Abstract

An analogy between crowd synchrony and multi-layer neural network architectures is proposed. It indicates that many non-identical dynamical elements (oscillators) communicating indirectly via a few mediators (hubs) can synchronize when the number of delayed couplings to the hubs or the strength of the couplings is large enough. This phenomenon is modeled using a system of semiconductor lasers optically delay-coupled in either a fully connected or a diluted manner to a fixed number of non-identical central hub lasers. A universal phase transition to crowd synchrony with hysteresis is observed, where the time to achieve synchronization diverges near the critical coupling independent of the number of hubs.

OCIS Codes
(190.3100) Nonlinear optics : Instabilities and chaos
(200.4700) Optics in computing : Optical neural systems
(270.3100) Quantum optics : Instabilities and chaos
(060.4258) Fiber optics and optical communications : Networks, network topology
(060.4263) Fiber optics and optical communications : Networks, star

ToC Category:
Optics in Computing

History
Original Manuscript: June 11, 2012
Manuscript Accepted: July 28, 2012
Published: August 13, 2012

Citation
Elad Cohen, Michael Rosenbluh, and Ido Kanter, "Phase transition in crowd synchrony of delay-coupled multilayer laser networks," Opt. Express 20, 19683-19689 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-18-19683

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References

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Arenas, A.
Blatt, M.
Boccaletti, S.
Bracikowski, C.
Buldú, J. M.
d’Ovidio, F.
Dallard, P.
Danino, T.
Danø, S.
De Monte, S.
Domany, E.
Elowitz, M. B.
Fitzpatrick, A.
Flint, A.
Garcia-Ojalvo, J.
Gómez, S.
Gómez-Gardeñes, J.
Gross, D. J.
Grossmann, T.
Hasty, J.
Huang, Z.
Jaimes-Reátegui, R.
James, G.
Kanter, I.
Kirkpatrick, T. R.
Le Bourva, S.
Leyva, I.
Low, A.
Masoller, C.
Mondragón-Palomino, O.
Moreno, Y.
Opper, M.
Priel, A.
Ridsdill Smith, R.
Rosenblatt, F.
Roy, R.
Sendiña-Nadal, I.
Sevilla-Escoboza, R.
Showalter, K.
Sompolinsky, H.
Sørensen, P. G.
Strogatz, S. H.
Taylor, A. F.
Thirumalai, D.
Tinsley, M. R.
Tsimring, L.
Wang, F.
Wiesenfeld, K.
Willford, M.
Zamora-Munt, J.

Europhys. Lett.

M. Opper, “Learning in neural networks: Solvable dynamics,” Europhys. Lett.8(4), 389–392 (1989). [CrossRef]

Nature

T. Danino, O. Mondragón-Palomino, L. Tsimring, and J. Hasty, “A synchronized quorum of genetic clocks,” Nature463(7279), 326–330 (2010). [CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

A. Priel, M. Blatt, T. Grossmann, E. Domany, and I. Kanter, “Computational capabilities of restricted two-layered perceptrons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics50(1), 577–595 (1994). [CrossRef] [PubMed]

Phys. Rev. Lett.

T. R. Kirkpatrick and D. Thirumalai, “Dynamics of the structural glass transition and the p-spin-interaction spin-glass model,” Phys. Rev. Lett.58(20), 2091–2094 (1987). [CrossRef] [PubMed]
D. J. Gross, I. Kanter, and H. Sompolinsky, “Mean-field theory of the Potts glass,” Phys. Rev. Lett.55(3), 304–307 (1985). [CrossRef] [PubMed]
J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett.105(26), 264101 (2010). [CrossRef] [PubMed]
K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, “Observation of antiphase states in a multimode laser,” Phys. Rev. Lett.65(14), 1749–1752 (1990). [CrossRef] [PubMed]
J. Gómez-Gardeñes, S. Gómez, A. Arenas, and Y. Moreno, “Explosive synchronization transitions in scale-free networks,” Phys. Rev. Lett.106(12), 128701 (2011). [CrossRef] [PubMed]
I. Leyva, R. Sevilla-Escoboza, J. M. Buldú, I. Sendiña-Nadal, J. Gómez-Gardeñes, A. Arenas, Y. Moreno, S. Gómez, R. Jaimes-Reátegui, and S. Boccaletti, “Explosive first-order transition to synchrony in networked chaotic oscillators,” Phys. Rev. Lett.108(16), 168702 (2012). [CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

J. Garcia-Ojalvo, M. B. Elowitz, and S. H. Strogatz, “Modeling a synthetic multicellular clock: repressilators coupled by quorum sensing,” Proc. Natl. Acad. Sci. U.S.A.101(30), 10955–10960 (2004). [CrossRef] [PubMed]
S. De Monte, F. d’Ovidio, S. Danø, and P. G. Sørensen, “Dynamical quorum sensing: Population density encoded in cellular dynamics,” Proc. Natl. Acad. Sci. U.S.A.104(47), 18377–18381 (2007). [CrossRef] [PubMed]

Psychol. Rev.

F. Rosenblatt, “The perceptron: A probabilistic model for information storage and organization in the brain,” Psychol. Rev.65(6), 386–408 (1958). [CrossRef] [PubMed]

Science

A. F. Taylor, M. R. Tinsley, F. Wang, Z. Huang, and K. Showalter, “Dynamical quorum sensing and synchronization in large populations of chemical oscillators,” Science323(5914), 614–617 (2009). [CrossRef] [PubMed]

Structural Engineer

P. Dallard, A. Fitzpatrick, A. Flint, S. Le Bourva, A. Low, R. Ridsdill Smith, and M. Willford, “The London millennium footbridge,” Structural Engineer79, 17–21 (2001).

Other

G. Bertotti, Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers (Academic Press, 1998).
S. H. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion, 2003).
A. Engel and C. Broeck, Statistical Mechanics of Learning (Cambridge Univ Press, 2001).
M. Opper and W. Kinzel, “Statistical mechanics of generalization,” in Models of Neural Networks III, E. D. J. L. van Hemmen, and K. Schulten, ed. (Springer-Verlag, 1996), 151–209.

2012, Leyva, Phys. Rev. Lett.
2011, Gómez-Gardeñes, Phys. Rev. Lett.
2010, Danino, Nature
2010, Zamora-Munt, Phys. Rev. Lett.
2009, Taylor, Science
2007, De Monte, Proc. Natl. Acad. Sci. U.S.A.
2004, Garcia-Ojalvo, Proc. Natl. Acad. Sci. U.S.A.
2001, Dallard, Structural Engineer
1994, Priel, Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics
1990, Wiesenfeld, Phys. Rev. Lett.
1989, Opper, Europhys. Lett.
1987, Kirkpatrick, Phys. Rev. Lett.
1985, Gross, Phys. Rev. Lett.
1958, Rosenblatt, Psychol. Rev.

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