No Access Submitted: 24 September 2018 Accepted: 06 October 2018 Published Online: 24 October 2018
Chaos 28, 101103 (2018); https://doi.org/10.1063/1.5062268
We study how nonlinear delayed-feedback in the Ikeda model can induce solitary impulses, i.e., dissipative solitons. The states are clearly identified in a virtual space-time representation of the equations with delay, and we find that conditions for their appearance are bistability of a nonlinear function and negative character of the delayed feedback. Both dark and bright solitons are identified in numerical simulations and physical electronic experiment, showing an excellent qualitative correspondence and proving thereby the robustness of the phenomenon. Along with single spiking solitons, a variety of compound soliton-based structures is obtained in a wide parameter region on the route from the regular dynamics (two quiescent states) to developed spatiotemporal chaos. The number of coexisting soliton-based states is fast growing with delay, which can open new perspectives in the context of information storage.
This work was supported by Russian Ministry of Education and Science (Project Code 3.8616.2017/8.9). We are grateful to Laurent Larger, Arkady Pikovsky, and Serhiy Yanchuk for illuminating discussions. We also acknowledge support and hospitality of Institute FEMTO-ST of Besancon, Technical University of Berlin, and University of Potsdam.
  1. 1. S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990). https://doi.org/10.1103/PhysRevLett.64.282, Google ScholarCrossref
  2. 2. B. S. Kerner and V. V. Osipov, Autosolitons: A New Approach to Problems of Self-Organization and Turbulence (Springer, 1994). Google ScholarCrossref
  3. 3. C. I. Christov and M. G. Velarde, Physica D 86, 323 (1995). https://doi.org/10.1016/0167-2789(95)00111-G, Google ScholarCrossref
  4. 4. F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, Phys. Rev. Lett. 115, 043902 (2015). https://doi.org/10.1103/PhysRevLett.115.043902, Google ScholarCrossref
  5. 5. Dissipative Solitons: From Optics to Biology and Medicine, edited by N. Akhmediev and A. Ankiewicz (Springer, 2008). Google Scholar
  6. 6. H. G. Purwins, H. U. Bödeker, and S. Amiranashvili, Adv. Phys. 59, 485 (2010). https://doi.org/10.1080/00018732.2010.498228, Google ScholarCrossref, ISI
  7. 7. A. W. Liehr, Dissipative Solitons in Reaction Diffusion Systems (Springer, 2013). Google ScholarCrossref
  8. 8. Soliton-driven Photonics, edited by A. D. Boardman and A. P. Sukhorukov (Springer, 2001). Google Scholar
  9. 9. F. Haudin, R. Rojas, U. Bortolozzo, S. Residori, and M. Clerc, Phys. Rev. Lett. 107, 264101 (2011). https://doi.org/10.1103/PhysRevLett.107.264101, Google ScholarCrossref
  10. 10. P. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012). https://doi.org/10.1038/nphoton.2011.345, Google ScholarCrossref
  11. 11. N. Verschueren, U. Bortolozzo, M. Clerc, and S. Residori, Phys. Rev. Lett. 110, 104101 (2013). https://doi.org/10.1103/PhysRevLett.110.104101, Google ScholarCrossref
  12. 12. B. Garbin, J. Javaloyes, G. Tissoni, and S. Barland, Nat. Commun. 6, 5915 (2015). https://doi.org/10.1038/ncomms6915, Google ScholarCrossref
  13. 13. M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, Nat. Photonics 9, 450 (2015). https://doi.org/10.1038/nphoton.2015.92, Google ScholarCrossref, ISI
  14. 14. J. Javaloyes, M. Marconi, and M. Giudici, Phys. Rev. Lett. 119, 033904 (2017). https://doi.org/10.1103/PhysRevLett.119.033904, Google ScholarCrossref, ISI
  15. 15. C. H. Wong and Y. Tserkovnyak, Phys. Rev. B 81, 060404 (2010). https://doi.org/10.1103/PhysRevB.81.060404, Google ScholarCrossref
  16. 16. S. V. Grishin, E. N. Beginin, M. A. Morozova, Y. P. Sharaevskii, and S. A. Nikitov, J. Appl. Phys. 115, 053908 (2014). https://doi.org/10.1063/1.4864133, Google ScholarScitation, ISI
  17. 17. A. V. Tur, A. V. Chechkin, and V. V. Yanovsky, Phys. Fluids B 4, 3513 (1992). https://doi.org/10.1063/1.860359, Google ScholarScitation, ISI
  18. 18. S. Ghost, A. Adak, and M. Khan, Phys. Plasmas 21, 012303 (2014). https://doi.org/10.1063/1.4862033, Google ScholarScitation
  19. 19. S. Sultana and I. Kourakis, Phys. Plasmas 22, 102302 (2015). https://doi.org/10.1063/1.4932071, Google ScholarScitation, ISI
  20. 20. B. Lautrup, R. Appali, A. D. Jackson, and T. Heimburg, Eur. Phys. J. E 34, 57 (2011). https://doi.org/10.1140/epje/i2011-11057-0, Google ScholarCrossref
  21. 21. N. Akhmediev, J. M. Soto-Crespo, and H. R. Brand, Phys. Lett. A 377, 968 (2013). https://doi.org/10.1016/j.physleta.2013.02.015, Google ScholarCrossref
  22. 22. S. Kai and H. Miike, Physica A 204, 346 (1994). https://doi.org/10.1016/0378-4371(94)90436-7, Google ScholarCrossref
  23. 23. S. Kai, T. Ariyoshi, S. Inenaga, and H. Miike, Physica D 84, 269 (1995). https://doi.org/10.1016/0167-2789(95)00023-W, Google ScholarCrossref
  24. 24. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon Press, 1995). Google Scholar
  25. 25. P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson et al., Nature 546, 274 (2017). https://doi.org/10.1038/nature22387, Google ScholarCrossref
  26. 26. Collision-Based Computing, edited by A. Adamatzky (Springer, 2002). Google Scholar
  27. 27. L. Larger, M. Soriano, D. Brunner, L. Appeltant, J. Gutierrez, L. Pesquera, C. Mirasso, and I. Fisher, Opt. Express 20, 3241 (2012). https://doi.org/10.1364/oe.20.003241, Google ScholarCrossref
  28. 28. Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, Sci. Rep. 2, 287 (2012). https://doi.org/10.1038/srep00287, Google ScholarCrossref
  29. 29. F. T. Arecchi, G. Giacomelli, A. Lapucci, and R. Meucci, Phys. Rev. A 45, R4225 (1992). https://doi.org/10.1103/PhysRevA.45.R4225, Google ScholarCrossref, ISI
  30. 30. G. Giacomelli and A. Politi, Phys. Rev. Lett. 76, 2686 (1996). https://doi.org/10.1103/PhysRevLett.76.2686, Google ScholarCrossref, ISI
  31. 31. R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, Phys. Rev. Lett. 108, 244101 (2012). https://doi.org/10.1103/PhysRevLett.108.244101, Google ScholarCrossref, ISI
  32. 32. L. Larger, A. Baylón-Fuentes, R. Martinenghi, V. S. Udaltsov, Y. K. Chembo, and M. Jacquot, Phys. Rev. X 7, 011015 (2017). https://doi.org/10.1103/PhysRevX.7.011015, Google ScholarCrossref
  33. 33. B. Romeira, R. Avó, J. M. L. Figueiredo, S. Barland, and J. Javaloyes, Sci. Rep. 6, 19510 (2016). https://doi.org/10.1038/srep19510, Google ScholarCrossref
  34. 34. S. Yanchuk and G. Giacomelli, J. Phys. A 50, 103001 (2017). https://doi.org/10.1088/1751-8121/50/10/103001, Google ScholarCrossref
  35. 35. D. Brunner, B. Penkovsky, R. Levchenko, E. Schöll, L. Larger, and Y. Maistrenko, Chaos 28, 103106 (2018). https://doi.org/10.1063/1.5043391, Google ScholarScitation
  36. 36. A. Vladimirov and D. Turaev, Phys. Rev. A 72, 033808 (2005). https://doi.org/10.1103/PhysRevA.72.033808, Google ScholarCrossref, ISI
  37. 37. M. Nizette, D. Rachinskii, A. Vladimirov, and M. Wolfrum, Physica D 218, 95 (2006). https://doi.org/10.1016/j.physd.2006.04.013, Google ScholarCrossref
  38. 38. D. Puzyrev, A. Vladimirov, S. Gurevich, and S. Yanchuk, Phys. Rev. A 93, 041801 (2016). https://doi.org/10.1103/PhysRevA.93.041801, Google ScholarCrossref
  39. 39. L. Larger, B. Penkovsky, and Y. Maistrenko, Phys. Rev. Lett. 111, 054103 (2013). https://doi.org/10.1103/PhysRevLett.111.054103, Google ScholarCrossref, ISI
  40. 40. L. Larger, B. Penkovsky, and Y. Maistrenko, Nat. Commun. 6, 7752 (2015). https://doi.org/10.1038/ncomms8752, Google ScholarCrossref, ISI
  41. 41. G. Giacomelli, F. Marino, M. A. Zaks, and S. Yanchuk, Europhys. Lett. 99, 58005 (2012). https://doi.org/10.1209/0295-5075/99/58005, Google ScholarCrossref
  42. 42. R. Manella, Int. J. Mod. Phys. C 13, 1177 (2002). https://doi.org/10.1142/S0129183102004042, Google ScholarCrossref
  43. 43. V. Semenov, A. Zakharova, Y. Maistrenko, and E. Schöll, Europhys. Lett. 115, 10005 (2016). https://doi.org/10.1209/0295-5075/115/10005, Google ScholarCrossref
  44. 44. V. V. Semenov, Chaos Solitons Fractals 116, 358 (2018). https://doi.org/10.1016/j.chaos.2018.09.045, Google ScholarCrossref
  45. 45. Y. Kivshar and G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003). Google Scholar
  46. 46. D. Luchinsky, P. V. E. McClintock, and M. Dykman, Rep. Prog. Phys. 61, 889 (1998). https://doi.org/10.1088/0034-4885/61/8/001, Google ScholarCrossref
  47. 47. F. Marino, G. Giacomelli, and S. Barland, Phys. Rev. Lett. 112, 103901 (2014). https://doi.org/10.1103/PhysRevLett.112.103901, Google ScholarCrossref, ISI
  48. 48. F. Marino, G. Giacomelli, and S. Barland, Phys. Rev. E 95, 052204 (2017). https://doi.org/10.1103/PhysRevE.95.052204, Google ScholarCrossref
  1. © 2018 Author(s). Published by AIP Publishing.