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Makarov V. V., Koronovskii A. A., Kurkin S. A., Levin Y. I., Moskalenko O. I., Maksimenko V. A., Hramov A. E., Balanov A. G. Bifurcations and transitions to chaos in superlattice coupled to external resonator. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 5, pp. 40-50. DOI: 10.18500/0869-6632-2013-21-5-40-50

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Bifurcations and transitions to chaos in superlattice coupled to external resonator

Makarov Vladimir Vladimirovich, Saratov State University
Koronovskii Aleksei Aleksandrovich, Saratov State University
Kurkin Semen Andreevich, Innopolis University
Levin Yurij Ivanovich, Saratov State University
Moskalenko Olga Igorevna, Saratov State University
Maksimenko Vladimir Aleksandrovich, Immanuel Kant Baltic Federal University
Hramov Aleksandr Evgenevich, Immanuel Kant Baltic Federal University
Balanov Aleksandr Gennadevich, Loughborough University

In this letter we study nonlinear dynamics and transition to chaos in semiconductor superlattice coupled to external linear resonator. We have shown that such system demonstrates chaotic dynamics in wide range of supply voltage, whereas in autonomous superlattice only periodical dynamics exists. Revealed that transition to chaos in system goes through intermittency

  1. Esaki L, Tsu R. Superlattices and negative differential conductivity in semiconductors. IBM Journal of Research and Development. 1970;14(1):61–65. DOI: 10.1147/rd.141.0061.
  2. Tsu R. Superlattices to Nanoelectronics. Elsevier. 2005.
  3. Ovsyannikov MI, Romanov YA, Shabanov VN, Loginova RG. Semiconductor periodic structures. Soviet physics. Semiconductors. 1970;4(12):2225–2231.
  4. Shic AYA. Superlattice-periodic semiconductor structures. Soviet physics. Semiconductors. 1974;8(10):1841–1864.
  5. Bonilla LL, Grahn HT. Non-linear dynamics of semiconductor superlattices. Rep. Prog. Phys. 2005;68(3):577–683. DOI:10.1088/0034-4885/68/3/R03.
  6. Fromhold TM, Patane A, Bujkiewicz S. et al. Chaotic electron diffusion through stochastic webs enhances current flow in superlattices. Nature. 2004;428(6984):726–730. DOI: 10.1038/nature02445.
  7. Balanov AG, Fowler D, Patane A, Eaves L, Fromhold TM. Bifurcations and chaos in semiconductor superlattices with a tilted magnetic field. Phys. Rev. E. 2008;77(2):026209. DOI: 10.1103/PhysRevE.77.026209.
  8. Selskii AO, Koronovskii AA, Hramov AE. et al. Effect of temperature on resonant electron transport through stochastic conduction channels in superlattices. Phys. Rev. B. 2011;84(23):235311. DOI: 10.1103/PhysRevB.84.235311.
  9. Balanov AG, Greenaway MT, Koronovsky AA. et al. The effect of temperature on the nonlinear dynamics of charge in a semiconductor superlattice in the presence of a magnetic field. Journal of Experimental and Theoretical Physics. 2012;114(5):836–840. DOI: 10.1134/S1063776112030132.
  10. Wacker A. Semiconductor superlattices: a model system for nonlinear transport. Physics Reports. 2002;357(1):1–111. DOI: 10.1016/S0370-1573(01)00029-1.
  11. Waschke C, Roskos HG, Schwedler R, Leo K, Kurz H, Kohler K. Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice. Phys. Rev. Lett. 1993;70(21):3319–3322. DOI: 10.1103/PhysRevLett.70.3319.
  12. Dmitriev AS, Panas AI, Starkov SO. Dynamic chaos as a paradigm of modern communication systems. Journal Achievements of Modern Radioelectronics. 1997;10:4–46.
  13. Dmitriev AS, Panas AI. Dynamic chaos: new media for communication systems. Moscow: Fizmatlit; 2002. 251 p. (In Russian).
  14. Koronovskii AA, Moskalenko OI, Hramov AE. On the use of chaotic synchronization for secure communication. Phys. Usp. 2009;52(12):1213–1238. DOI: 10.3367/UFNr.0179.200912c.1281.
  15. Trubetskov DI, Kuznetsov SP, Ryskin NM, Temples AE. Complex dynamics of distributed systems of ultra-high frequency electronics. Nonlinear Waves 2004. Ed. Gaponov-Grekhov AV, Neorakin VI. Nizhny Novgorod: IAP RAS; 2005. 544 p. (In Russian).
  16. Dmitrieva TV, Ryskin NM, Titov VN, Shigaev AM. COMPLEX DYNAMICS OF SIMPLE MODELS OF EXTENDED ELECTRON-WAVE SYSTEMS. Izvestiya VUZ. Applied Nonlinear Dynamics. 1999;7(6):66–82.
  17. Kuznetsov SP. Nonlinear dynamics of backward-wave tube: self-modulation, multi-stability, control. Izvestiya VUZ. Applied Nonlinear Dynamics. 2006;14(4):3–35. DOI: 10.18500/0869-6632-2006-14-4-3-35.
  18. Nusinovich GS, Vlasov AN, Antonsen TM. Nonstationary phenomena in tapered gyro-backward-wave oscillators. Phys.Rev.Lett. 2001;87(21):218301. DOI: 10.1103/PhysRevLett.87.218301.
  19. Hramov AE, Koronovskii AA, Kurkin SA. et al. Effect of a resonator on high-frequency electron dynamics in semiconductor superlattices. Submitted to Phys.Rev.Lett. 2013;77(12):1744–1747. DOI: 10.3103/S1062873813120083.
  20. Takens F. Detecting strange attractors in dynamical systems and turbulence. In book «Lectures Notes in Mathematics». Eds D. Rand and L-S. Young. New-York: Springler– Verlag; 1981. 366–381 p.
  21. Berger P, Pomo I, Vidal K. Order in chaos. Moscow: Mir; 1991. 368 p. (In Russian).
  22. Рабинович МИ, Трубецков ДИ. Введение в теорию колебаний и волн. Мoscow-Izhevsk: RCD; 2000. 560 p. (In Russian).
  23. Materassi D, Basso M. Time scaling of chaotic systems: Application to secure communications. International Journal of Bifurcation and Chaos. 2008;18(2):567–575.
  24. Moskalenko OI, Koronovskii AA, Hramov AE. Generalized synchronization of chaos for secure communication: Remarkable stability to noise. Phys. Lett. A. 2010;374(29):2925–2931. DOI: 10.1016/j.physleta.2010.05.024.
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