Characterizing the hyperchaotic dynamics of a semiconductor laser subject to optical feedback via permutation entropy

IEEE Journal on Selected Topics in Quantum Electronics

Volumn 17, Issue 5, 2011, Pages 1250-1257

  Zunino, Luciano ^a   Rosso, Osvaldo A ^b,c   Soriano, Miguel C ^d  

^a Centro de Investigaciones Opticas CONICET la Plata CIC   (Argentina)

^b FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

^c INSTITUTO DE CÁLCULO   (Argentina)

^d INSTITUTO DE FÍSICA INTERDISCIPLINAR Y SISTEMAS COMPLEJOS IFISC CSIC UIB   (Spain)

Author keywords

Chaos; degree of unpredictability; optical feedback; permutation entropy; semiconductor lasers

Indexed keywords

CHAOS QUANTIFIERS; CHAOTIC FLUCTUATIONS; CHAOTIC LASERS; DEGREE OF UNPREDICTABILITY; HIGH-DIMENSIONAL; HYPERCHAOTIC; KOLMOGOROV-SINAI ENTROPY; NOISY ENVIRONMENT; NUMERICAL RESULTS; PERMUTATION ENTROPY; TIME EVOLUTIONS; TIME-SCALES;

CHAOTIC SYSTEMS; DISTRIBUTION FUNCTIONS; ENTROPY; INFORMATION THEORY; LASERS; PROBABILITY DISTRIBUTIONS; RATING; SEMICONDUCTOR LASERS; TIME SERIES;

FEEDBACK;

EID: 80053933774     PISSN: 1077260X     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSTQE.2011.2145359     Document Type: Article

References (45)

1. S.Wieczorek, B. Krauskopf, and D. Lenstra, "A unifying view of bifurcations in a semiconductor laser subject to optical injection" Opt. Commun., vol. 172, pp. 279-295, 1999. (Pubitemid 30522880)
2. J. Mork, B. Tromborg, and J. Mark, "Chaos in semiconductor lasers with optical feedback: Theory and experiment" IEEE J. Quantum Electron., vol. 28, no. 1, pp. 93-108, Jan. 1992.
3. D. H. DeTienne, G. R. Gray, G. P. Agrawal, and D. Lenstra, "Semiconductor laser dynamics for feedback from a finite-penetration-depth phase-conjugate mirror" IEEE J. Quantum Electron., vol. 33, no. 5, pp. 838-844, May 1997. (Pubitemid 127559655)
4. J.-P. Goedgebuer, L. Larger, and H. Porte, "Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode" Phys. Rev. Lett., vol. 80, pp. 2249-2252, 1998. (Pubitemid 128621539)
5. M. Yousefi and D. Lenstra, "Dynamical behavior of a semiconductor laser with filtered external optical feedback" IEEE J. Quantum Electron., vol. 35, no. 6, pp. 970-976, Jun. 1999.
6. I. Fischer, O. Hess,W. Elsässer, and E. Göbel, "High-dimensional chaotic dynamics of an external cavity semiconductor laser" Phys. Rev. Lett., vol. 73, pp. 2188-2191, 1994. (Pubitemid 24979576)
7. R. Vicente, J. Daud'en, P. Colet, and R. Toral, "Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop" IEEE J. Quantum Electron., vol. 41, no. 4, pp. 541-548, Apr. 2005. (Pubitemid 40555786)
8. C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, "Synchronization of chaotic semiconductor lasers: Application to encoded communications" IEEE Photon. Technol. Lett., vol. 8, no. 2, pp. 299-301, Feb. 1996. (Pubitemid 126546859)
9. V. Annovazzi-Lodi, S. Donati, and A. Scir'e, "Synchronization of chaotic injected-laser systems and its application to optical cryptography" IEEE J. Quantum Electron., vol. 32, no. 6, pp. 953-959, Jun. 1996. (Pubitemid 126530098)
10. G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers" Science, vol. 279, pp. 1198-1200, 1998. (Pubitemid 28164369)
11. J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback" IEEE J. Quantum Electron., vol. 38, no. 9, pp. 1141-1154, Sep. 2002. (Pubitemid 35032638)
12. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garc'ia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fibreoptic links" Nature, vol. 438, pp. 343-346, 2005. (Pubitemid 41643948)
13. V. S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, P. Levy, and W. T. Rhodes, "Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations" Phys. Lett. A, vol. 308, pp. 54-60, 2003.
14. M. C. Soriano, P. Colet, and C. R.Mirasso, "Security implications of openand closed-loop receivers in all-optical chaos-based communications" IEEE Photon. Technol. Lett., vol. 21, no. 7, pp. 426-428, Apr. 2009.
15. A. Jacobo, M. C. Soriano, C. R. Mirasso, and P. Colet, "Chaos-based optical communications: encryption versus nonlinear filtering" IEEE J. Quantum Electron., vol. 46, no. 4, pp. 499-505, Apr. 2010.
16. R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties" IEEE J. Quantum Electron., vol. 16, no. 3, pp. 347-355, Mar. 1980. (Pubitemid 10468454)
17. M. S. Baptista, E. J. Ngamga, P. R. F. Pinto, M. Brito, and J. Kurths, "Kolmogorov-Sinai entropy from recurrence times" Phys. Lett. A, vol. 374, pp. 1135-1140, 2010.
18. A. W. Jayawardena, P. Xu, and W. K. Li, "Modified correlation entropy estimation for a noisy chaotic time series" Chaos, vol. 20, pp. 0231041-02310411, 2010.
19. C. Bandt and B. Pompe, "Permutation entropy: A natural complexity measure for time series" Phys. Rev. Lett., vol. 88, pp. 1741021-1741024, 2002. (Pubitemid 34555146)
20. Y. Cao, W. Tung, J. B. Gao, V. A. Protopopescu, and L. M. Hively, "Detecting dynamical changes in time series using the permutation entropy" Phys. Rev. E, vol. 70, pp. 0462171-0462177, 2004.
21. L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, "Permutation-information-theory approach to unveil delay dynamics from time-series analysis" Phys. Rev. E, vol. 82, pp. 0462121-0462129, 2010.
22. M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, "Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis" IEEE J. Quantum Electron., vol. 47, no. 2, pp. 252-261, Feb. 2011.
23. M. Staniek and K. Lehnertz, "Parameter selection for permutation entropy measurements" Int. J. Bifurcation Chaos, vol. 17, pp. 3729-3733, 2007.
24. X. Li, G. Ouyang, and D. A. Richards, "Predictability analysis of absence seizures with permutation entropy" Epilepsy Res., vol. 77, pp. 70-74, 2007. (Pubitemid 47588843)
25. L. Zunino, D. G. P'erez, M. T. Mart'in, M. Garavaglia, A. Plastino, and O. A. Rosso, "Permutation entropy of fractional Brownian motion and fractional Gaussian noise" Phys. Lett. A, vol. 372, pp. 4768-4774, 2008.
26. X. Li, S. Cui, and L. J. Voss, "Using permutation entropy to measure the electroencephalographic effects of sevoflurane" Anesthesiology, vol. 109, pp. 448-456, 2008.
27. M. Matilla-Garc'ia and M. Ruiz Mar'in, "A non-parametric independence test using permutation entropy" J. Econometrics, vol. 144, pp. 139-155, 2008.
28. O. A. Rosso and C. Masoller, "Detecting and quantifying stochastic and coherence resonances via information-theory complexity measurements" Phys. Rev. E, vol. 79, pp. 040106R1-040106R4, 2009.
29. L. Zunino, M. Zanin, B. M. Tabak, D. G. P'erez, and O. A. Rosso, "Forbidden patterns, permutation entropy and stock market inefficiency" Physica A, vol. 388, pp. 2854-2864, 2009.
30. L. D. Micco,H.A. Larrondo, A. Plastino, andO.A.Rosso, "Quantifiers for randomness of chaotic pseudo-random number generators" Phil. Trans. R. Soc. A, vol. 367, pp. 3281-3296, 2009.
31. O. A. Rosso,H.A. Larrondo, M. T. Mart'in,A. Plastino, andM.A. Fuentes, "Distinguishing noise from chaos" Phys. Rev. Lett., vol. 99, pp. 154102 1-1541024, 2007.
32. J. M. Amig'o,S.Zambrano, andM.A. F. Sanju'an, "True and false forbidden patterns in deterministic and random dynamics" Europhys. Lett., vol. 79, p. 50001, 2007.
33. F. M. Atay, S. Jalan, and J. Jost, "Randomness, chaos, and structure" Complexity, vol. 15, pp. 29-35, 2009.
34. X. Li and G. Ouyang, "Estimating coupling direction between neuronal populations with permutation conditional mutual information" Neuroimage, vol. 52, pp. 497-507, 2010.
35. C. Bandt, "Ordinal time series analysis" Ecological Modell., vol. 182, pp. 229-238, 2005. (Pubitemid 40205670)
36. M. T. Rosenstein, J. J. Collins, and C. J. De Luca, "A practical method for calculating largest Lyapunov exponents from small data sets" Physica D, vol. 65, pp. 117-134, 1993.
37. K. E. Chlouverakis, A. Argyris, A. Bogris, and D. Syvridis, "Complexity and synchronization in chaotic fiber-optic systems" Physica D, vol. 237, pp. 568-572, 2008. (Pubitemid 351324840)
38. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis. Cambridge, U.K.: Cambridge Univ. Press, 2004.
39. J. D. Farmer, "Chaotic attractors of an infinite-dimensional dynamical system" Physica D, vol. 4, pp. 366-393, 1982.
40. R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, "Identifying and modeling delay feedback systems" Phys. Rev. Lett., vol. 81, pp. 558-561, 1998. (Pubitemid 128628313)
41. M. J. Bünner, M. Ciofini, A. Giaquinta, R. Hegger, H. Kantz, R. Meucci, and A. Politi, "Reconstruction of systems with delayed feedback-Part I: Theory" Eur. Phys. J. D, vol. 10, pp. 165-176, 2000.
42. M. J. Bünner, M. Ciofini, A. Giaquinta, R. Hegger, H. Kantz, R. Meucci, and A. Politi, "Reconstruction of systems with delayed feedback-Part II: Application" Eur. Phys. J. D, vol. 10, pp. 177-187, 2000.
43. K.Keller andM. Sinn, "A standardized approach to theKolmogorov-Sinai entropy" Nonlinearity, vol. 22, pp. 2417-2422, 2009.
44. K. Keller and M. Sinn, "Kolmogorov-Sinai entropy from the ordinal viewpoint" Physica D, vol. 239, pp. 997-1000, 2010.
45. C. Bandt, G. Keller, and B. Pompe, "Entropy of interval maps via permutations" Nonlinearity, vol. 15, pp. 1595-1602, 2002. (Pubitemid 37023485)