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Overlapping Adding-Doubling Spikes Cascades in a Semiconductor Laser Proxy

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Abstract

A study of the distribution of spikes in periodic oscillations is reported for an optically injected laser diode proxy, as a function of the injected field strength and detuning. A novel and unexpected feature reported here is an abundance of overlapping adding-doubling complexification cascades. Two-parameter spikes complexification cascades of the laser proxy are found to mimic phenomena also found in a state-of-the-art semiconductor laser model. Such cascades should not be difficult to observe experimentally, either in lasers or in other complex oscillators.

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References

  1. M.R. Gallas, M.R. Gallas, J.A.C. Gallas, Distribution of chaos and periodic spikes in a three-cell population model of cancer. Eur. Phys. J. Special Topics 223, 2131–2144 (2014)

    Article  ADS  Google Scholar 

  2. X.B. Rao, X.P. Zhao, J.S. Gao, J.G. Zhang, Self-organization with fast-slow time scale dynamics in a memristor-based Shinriki’s circuit. Commun. Nonlin. Sci. Num. Simul. 94, 105569 (2021)

    Article  Google Scholar 

  3. X.B. Rao, Y.D. Chu, L. Xu, Y.X. Chang, J.G. Zhang, Fractal structures in centrifugal flywheel governor system. Commun. Nonlin. Sci. Num. Simul. 50, 330–339 (2017)

    Article  MathSciNet  Google Scholar 

  4. L. Xu, Y.D. Chu, Q. Yang, Novel dynamical scenario of the two-stage Colpitts oscillator, Chaos. Sol. Fractals 138, 109998 (2020)

    Article  Google Scholar 

  5. J.A. Vélez, J. Bragard, L.M. Pérez, A.M. Cabanas, O.J. Suarez, D. Laroze, H.L. Mancini, Periodicity characterization of the nonlinear magnetization dynamics. Chaos 30, 093112 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  6. C.S. Rodrigues, C.G.P. dos Santos, C.C. de Miranda, E. Parma, H. Varela, R. Nagao, A numerical investigation of the effect of external resistence and applied potential on the distribution of periodicity and chaos in the anodic dissolution of nickel. Phys. Chem. Chem. Phys. 22, 21823 (2020)

    Article  Google Scholar 

  7. X.F. Li, A.Y.T. Leung, Y.D. Chu, Symmetry and period-adding windows in a modified optical injection semiconductor laser model. Chin. Phys. Lett. 29, 010201 (2012)

    Article  ADS  Google Scholar 

  8. S. Wieczorek, B. Krauskopf, T.B. Simpson, D. Lenstra, The dynamical complexity of optically injected semiconductor lasers. Phys. Rep. 416, 1–128 (2005)

    Article  ADS  Google Scholar 

  9. C. Bonatto, J.A.C. Gallas, Accumulations horizons and period adding cascades in optically injected semiconductor lasers. Phys. Rev. E 75, 055204(R) (2007)

    Article  ADS  Google Scholar 

  10. C. Bonatto, J.A.C. Gallas, Accumulation boundaries: Codimension-two accumulation of accumulations in phase diagrams of semiconductor lasers, electric circuits, atmospheric, and chemical oscillators. Phil. Trans. Royal Soc. London, Series A 366, 505-517 (2008)

  11. V. Kovanis, A. Gavrielides, J.A.C. Gallas, Labyrinth bifurcations in optically injected diode lasers. Eur. Phys. J. D 58, 181–186 (2010)

    Article  ADS  Google Scholar 

  12. G.P. Agrawal, C.M. Bowden, Concept of linewidth enhancement factor in semiconductor lasers: usefulness and limitations. IEEE Photonics Technology Letters 5, 640–642 (1993)

    Article  ADS  Google Scholar 

  13. C. Bonatto, J.A.C. Gallas, Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit. Phys. Rev. Lett. 101, 054101 (2008)

    Article  ADS  Google Scholar 

  14. R. Vitolo, P. Glendinning, J.A.C. Gallas, Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows. Phys. Rev. E 84, 016216 (2011)

    Article  ADS  Google Scholar 

  15. J. Freire, J.A.C. Gallas, Stern-Brocot trees in the periodicity of mixed-mode oscillations. Phys. Chem. Chem. Phys. 13, 12191–12198 (2011)

    Article  Google Scholar 

  16. J. Freire, J.A.C. Gallas, Stern-Brocot trees in cascades of mixed-mode oscillations and canards in the extended Bonhoeffer-van der Pol and the FitzHugh-Nagumo models of excitable systems. Phys. Lett. A 375, 1097–1103 (2011)

    Article  ADS  Google Scholar 

  17. J.A.C. Gallas, Spiking systematics in some CO\(_2\) laser models, Invited review chapter. Adv. Atom. Molec. Opt. Phys. 65, 127–191 (2016)

    Article  ADS  Google Scholar 

  18. J.A.C. Gallas, M.J.B. Hauser, L.F. Olsen, Complexity of a peroxidase-oxidase reaction model, Phys. Chem. Chem. Phys. 23, 1943-1945 (2021).

  19. J.A.C. Gallas, Structure of the parameter space of the Hénon map. Phys. Rev. Lett. 70, 2714–2717 (1993)

    Article  ADS  Google Scholar 

  20. E.N. Lorenz, Compound windows of the Hénon map. Physica D 237, 1689–1704 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  21. W. Façanha, B. Oldeman, L. Glass, Bifurcation structures in two-dimensional maps: The endoskeleton of shrimps. Phys. Lett. A 377, 1264–1268 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  22. M. Bier, T.C. Bountis, Remerging Feigenbaum trees in dynamical systems. Phys. Lett. A 104, 239–244 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  23. P. Ashwin, J. Buescu, I. Stewart, Bubbling of attractors and synchronization of chaotic oscillators. Phys. Lett. A 193, 126–139 (1994)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

This work was started during a visit to the Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany, in the framework of the Advanced Study Group Forecasting with Lyapunov vectors. The author was partially supported by CNPq, Brazil, grant 304719/2015-3. All bitmaps were computed at the CESUP-UFRGS Supercomputer Center of the Federal University in Porto Alegre, Brazil.

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Correspondence to Jason A. C. Gallas.

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Gallas, J.A.C. Overlapping Adding-Doubling Spikes Cascades in a Semiconductor Laser Proxy. Braz J Phys 51, 919–926 (2021). https://doi.org/10.1007/s13538-021-00865-z

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