Chaos and Mixed Mode Oscillations in Optoelectronic Networks


(*) Corresponding author


Authors' affiliations


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


We report the occurrence of synchronization of complex sequences of chaotic and periodic Mixed Mode Oscillations (MMOs) in light emitting diodes with optoelectronic feedback. In this study, we demonstrate that MMOs and chaotic spike sequences appearing in the context of incomplete homoclinic scenarios. The optoelectronic oscillators have been combined as a nearest neighbor configuration. We investigate the transition between non synchronization and synchronization states by means of the spatio-temporal distribution, entropy and the coherence.
Copyright © 2013 Praise Worthy Prize - All rights reserved.

Keywords


Chaos; MMOs; Synchronization; Network

Full Text:

PDF


References


L.M. Pecora and A.V.Carroll, Synchronization in chaotic systems,Phys. Rev. Lett., 64,8 ( 1990), 821-824.

A.T. Winfree, Biological rhythms and the behavior of populations of coupled oscillators,J. Theor. Biol 16 ( 1967) 15.

M.V. Ivanchenko, G.V. Osipov, V.D. Shalfeev, J. Kurths, Phase synchronization in ensembles of bursting oscillatorsPhys. Rev. Lett. 93(2004 ) 93, 134101.

T. Shibata, T. Ghawanya, K. Kaneko, Phys. Rev. Lett, 82 ( 1999), 4424.

P. Ostborn, Phase transition to frequency entrainment in a long chain of pulse-coupled oscillators, Phys. Rev. E, 66 ( 2002), 016105.

Bove I.; Boccaletti S.; Bragard J.; Kurths J.; and Mancini H., Phys. Rev. E, 2004, 69, 016208.

A. N. Pisarchik, R. Jaimes-Reategui, J.R. Villalobos-Salazar, J.H. Garcia-Lopez, and S. Boccaletti, Synchronization of chaotic sys- tems with coexisting attractors, Phys. Rev. Lett.96 ( 2006), 244102.

M. Ciszak, A. Montina, F.T. Arecchi, Sharp versus smooth synchronization transition in locally coupled oscillators, Phys. Rev. E, 78 (2008), 78, 016202.

Ostwald W. Z. Phys. Chem., Stoechiom. Verwandtschaftsl., 1900, 35, 33.

M. Bertram and A.S. Mikhailov, Pattern formation in a surface chemical reaction with global delayed feedback, Phys. Rev. E 63 (2001), 066102.

M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, Controlling turbulence in a surface chemical reaction by time-delay autosynchronization. Phys. Rev. E, 67 (2003), 046224

M. Kim, M. Bertram, et al., Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic CO oxidation on Pt( 1 10), Science 292 (2001) 1357

M.T.M. Koper, Bifurcations of mixed-mode oscillations in a three-variable autonomous Van der Pol-Duffing model with a cross-shaped phase diagram. Physica D, 80 (1995), 72-94 .

Plenge F. , Rodin P., Scholl E., and Krischer K., Breathing Current Domains in Globally Coupled Electrochemical Systems: A Comparison with a Semiconductor Model, Phys.Rev. E 64 (2001), 056229.

A.A. Alonso and R.R. Llins, Subthreshold Na -dependent theta-like rhythmic- ity in stellate cells of entorhinal cortex layer II, .Nature, 342 (1989), 175.

G.S. Medvedev and J.E. Cisternas, Multimodal regimes in a compartmental model of the dopamine neuron, Physica D , 194 (2004), 333.

U. L. F. Kummer. C. J. Olsen. A. K. Dixon E. Green. Bornberg-Bauer, and G. Baier, Switching from simple to complex oscillations in calcium signaling, Biophys. J, 79 (.2000), 1188 .

M. Mikikian, L. Couëdel, M. Cavarroc, Y. Tessier, L. Boufendi...in complex plasma instabilities. Phys. Rev. Lett. 100 (2008), 225005

K. Al Naimee, F. Marino, M. Ciszak, R. Meucci, F. T. Arecchi, Chaotic spiking and incomplete homoclinic scenarios in semiconductor lasers with optoelectronic feedback, New Journal of Physics, 11 (2009), 073022.

S. F. Abdalah, M. Ciszak, F. Marino, K. Al Naimee, R. Meucci, F. T. Arecchi, Noise Effects on Excitable Chaotic Attractors in Coupled Light-Emitting Diodes; IEEE system journal, 6 (2012), 558-563

S.F. Abdalah, M. Ciszak, F. Marino, K. Al Naimee, R. Meucci, F. T. Arecchi, Optoelectronic devices and properties ISBN 978-953-307-204-3, Intech,( 2011), 651.

F. Marino, M. Ciszak, S. F. Abdalah, K. Al Naimee, R. Meucci, F.T. Arecchi, Mixed-mode oscillations via canard explosions in light-emitting diodes with optoelectronic feedback, Phy. Rev. E. 84 (2011), 047201.

V. Petrov, S. K. Scott, and K. Showalter, Mixed-Mode Oscillations in Chemical Systems,, J. Chem. Phys. 97 (1992), 6191-6198

E. Izhikevich, Neural Excitability, Spiking, and Bursting, Int. J. Bifurcation Chaos, 10 (2000), 1171.

K. Al Naimee, F. Marino, M. Ciszak, S.F.Abdalah, R. Meucci and F. T. Arecchi, Excitability of periodic and chaotic attractors in semiconductor lasers with optoelectronic feedback, Eur. Phys. J. D , 58 (2010), 187–189.


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize