Advertisement

Implementation of a Laboratory-Based Educational Tool for Teaching Nonlinear Circuits and Chaos

  • A. E. Giakoumis
  • Ch. K. Volos
  • I. N. Stouboulos
  • I. M. Kyprianidis
  • H. E. Nistazakis
  • G. S. Tombras
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 636)

Abstract

The last three decades the subject of nonlinear circuits has become an interesting topic not only due to its applications in various fields but also for educational aims. In this direction, Chua’s circuit is considered a cornerstone because it is a unique platform both for the understanding of nonlinear phenomena and the study of experimental chaos as well. So, in this chapter, a new laboratory setup of Chua’s oscillator circuit is presented. The proposed realization is suitable for studying, in the laboratory, the design of a nonlinear circuit step by step. It is also a very useful tool for illustrating in the oscilloscope well-known phenomena related with chaos theory, such as period doubling route to chaos, crisis phenomena, intermittency, and attractors’ coexistence. The proposed platform could be a useful laboratory-based educational tool for teaching nonlinear circuits in courses related with nonlinear dynamics and chaos for undergraduate, postgraduate and Ph.D. students.

Keywords

Nonlinear circuit Chaos Chua’s oscillator Chua’s diode Period doubling route to chaos Crisis phenomena Intermittency Attractor’s coexistence 

References

  1. 1.
    Alligood KT, Sauer TD, Yorke JA (2000) Chaos: an introduction to dynamical systems. Springer, New YorkzbMATHGoogle Scholar
  2. 2.
    Anishchenko V, Safonova M, Chua LO (1992) Stochastic resonance in Chua’s circuit. Int J Bifurc Chaos 2:397–401MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Arns RG (1998) The other transistor: early history of the metal-oxide semiconductor field-effect transistor. Eng Sci Educ J 7(5):233–240CrossRefGoogle Scholar
  4. 4.
    Baker GL, Gollub JP (1990) Chaotic dynamics: an introduction. Cambridge University Press, CambridgezbMATHGoogle Scholar
  5. 5.
    Bier M, Bountis TC (1984) Remerging Feigenbaum trees in dynamical systems. Phys Lett A 104:239–244MathSciNetCrossRefGoogle Scholar
  6. 6.
    Brunetti C (1939) The transitron oscillator. Proc IRE 27(2):88–94CrossRefGoogle Scholar
  7. 7.
    Chen G, Ueta T (2002) Chaos in circuits and systems. World Scientific, SingaporezbMATHGoogle Scholar
  8. 8.
    Chua LO (1994) Chua’s circuit 10 year later. Int J Bifurc Chaos 22:279–305Google Scholar
  9. 9.
    Chua LO, Yu J, Yu Y (1983) Negative resistance devices. Int J Circuit Theory Appl 11:161–186CrossRefzbMATHGoogle Scholar
  10. 10.
    Chua LO, Wu CW, Huang A, Zhong GQ (1993) A universal circuit for studying and generating chaos—part I: routes to chaos. IEEE Trans Circuits Syst I 40(10):732–744Google Scholar
  11. 11.
    Chua LO, Wu CW, Huang A, Zhong GQ (1993) A universal circuit for studying and generating chaos—part II: strange attractors. IEEE Trans Circuits Syst I 40(10):745–761Google Scholar
  12. 12.
    Cruz JM, Chua LO (1992) A CMOS IC nonlinear resistor for Chua’s circuit. ERL Memorandum, Electronics Research Laboratory, University of California, BerkeleyGoogle Scholar
  13. 13.
    Dawson P, Grebogi C, Yorke J, Kan I (1992) Antimonotonicity-inevitable reversal of period doubling cascades. Phys Lett A 162:249–252MathSciNetCrossRefGoogle Scholar
  14. 14.
    Esaki L (1958) New phenomenon in narrow germanium p-n junctions. Phys Rev 109(2):603CrossRefGoogle Scholar
  15. 15.
    Field RJ, Györgyi L (1993) Chaos in chemistry and biochemistry. World Scientific Publishing, SingaporeCrossRefGoogle Scholar
  16. 16.
    Feigenbaum MJ (1979) The universal metric properties of nonlinear transformations. J Stat Phys 21:669–706MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Fortuna L, Frasca M, Xibilia MG (2009) Chua’s circuit implementations: yesterday, today and tomorrow. World Scientific, SingaporeGoogle Scholar
  18. 18.
    Grebogi C, Yorke J (1997) The impact of chaos on science and society. United Nations University Press, TokyoGoogle Scholar
  19. 19.
    Grebogi C, Ott E, Yorke JA (1983) Crises: sudden changes in chaotic attractors and chaotic transients. Phys D 7:181–200MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Halle K, Chua LO, Anishchenko V, Safonova M (1992) Signal amplification via chaos: experimental evidence. Int J Bifurc Chaos 2:1011–1020CrossRefzbMATHGoogle Scholar
  21. 21.
    Hasselblatt B, Katok A (2003) A first course in dynamics: with a panorama of recent developments. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  22. 22.
    Hull AW (1918) The dynatron: a vacuum tube possessing negative electric resistance. Proc Inst Radio Eng 6(1):5–35Google Scholar
  23. 23.
    Kennedy MP (1992) Robust op amp realization of Chua’s circuit. Frequenz 46(3–4):66–80Google Scholar
  24. 24.
    Kocarev L, Halle K, Eckert K, Chua LO (1993) Experimental observations of antimonotonicity in Chua’s circuit. Int J Bifurc Chaos 3:1051–1055CrossRefzbMATHGoogle Scholar
  25. 25.
    Kyprianidis IM, Fotiadou ME (2006) Complex dynamics in Chua’s canonical circuit with a cubic nonlinearity. WSEAS Trans Circuits Syst 5:1036–1043Google Scholar
  26. 26.
    Kyprianidis IM, Haralabidis P, Stouboulos IN, Bountis T (2000) Antimonotonicity and chaotic dynamics in a fourth order autonomous nonlinear electric circuit. Int J Bifurc Chaos 10:1903–1915Google Scholar
  27. 27.
    Kyrtsou C, Vorlow C (2005) Complex dynamics in macroeconomics: a novel approach. In: Diebolt C, Kyrtsou C (eds) New trends in macroeconomics. Springer, Berlin, pp 223–245. ISBN-13: 978-3-540-21448-9Google Scholar
  28. 28.
    Li TY, Yorke JA (1975) Period three implies chaos. Am Math Mon 82(10):985–992MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Lorenz EN (1963) Deterministic non-periodic flow. J Atmos Sci 20:130–141CrossRefGoogle Scholar
  30. 30.
    Mandelbrot B (1977) The fractal geometry of nature. W.H. Freeman Company, New YorkzbMATHGoogle Scholar
  31. 31.
    Matsumoto T (1984) A chaotic attractor from Chua’s circuit. IEEE Trans Circuits Syst CAS–31(12):1055–1058CrossRefzbMATHGoogle Scholar
  32. 32.
    Matsumoto T, Chua LO, Tokumasu K (1986) Double scroll via a two-transistor circuit. IEEE Trans Circuits Syst 33(8):828–835MathSciNetCrossRefGoogle Scholar
  33. 33.
    May RM (1976) Theoretical ecology: principles and applications. W.B. Saunders Company, PhiladelphiaGoogle Scholar
  34. 34.
    Moon FC (1987) Chaotic vibrations: an introduction for applied scientists and engineers. Wiley, New YorkzbMATHGoogle Scholar
  35. 35.
    Nicolis G (1995) Introduction to nonlinear science. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  36. 36.
    Ott E (1993) Chaos in dynamical systems. Cambridge University Press, CambridgezbMATHGoogle Scholar
  37. 37.
    Pivka L, Spany V (1993) Boundary surfaces and basin bifurcations in Chua’s circuit. J Circuits Syst Comput 3:441–470MathSciNetCrossRefGoogle Scholar
  38. 38.
    Poincaré JH (1890) Sur le probleme des trois corps et les equations de la dynamique. Divergence des series de M. Lindstedt. Acta Math 13:1–270Google Scholar
  39. 39.
    Rössler OE (1976) An equation for continuous chaos. Phys Lett 57A(5):397–398CrossRefGoogle Scholar
  40. 40.
    Strogatz SH (1994) Nonlinear dynamics and chaos. Addison-Wesley, New YorkGoogle Scholar
  41. 41.
    Turner LB (1920) The Kallirotron. An aperiodic negative-resitance triode combination. Radio Rev 1:317–329Google Scholar
  42. 42.
    Voelcker J (1989) The Gunn effect. IEEE Spectr 26(7). doi: 10.1109/6.29344
  43. 43.
    Zhong GQ, Ayron F (1985) Experimental confirmation of chaos from Chua’s circuit. Int J Circuit Theory Appl 13(11):93–98CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • A. E. Giakoumis
    • 1
  • Ch. K. Volos
    • 1
  • I. N. Stouboulos
    • 1
  • I. M. Kyprianidis
    • 1
  • H. E. Nistazakis
    • 2
  • G. S. Tombras
    • 2
  1. 1.Physics DepartmentAristotle University of ThessalonikiThessalonikiGreece
  2. 2.Faculty of Physics, Department of Electronics, Computers, Telecommunications and ControlNational and Kapodistrian University of AthensAthensGreece

Personalised recommendations