Skip to main content

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

  • Chapter
  • First Online:

Part of the book series: Studies in Computational Intelligence ((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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Alligood KT, Sauer TD, Yorke JA (2000) Chaos: an introduction to dynamical systems. Springer, New York

    MATH  Google Scholar 

  2. Anishchenko V, Safonova M, Chua LO (1992) Stochastic resonance in Chua’s circuit. Int J Bifurc Chaos 2:397–401

    Article  MathSciNet  MATH  Google Scholar 

  3. Arns RG (1998) The other transistor: early history of the metal-oxide semiconductor field-effect transistor. Eng Sci Educ J 7(5):233–240

    Article  Google Scholar 

  4. Baker GL, Gollub JP (1990) Chaotic dynamics: an introduction. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  5. Bier M, Bountis TC (1984) Remerging Feigenbaum trees in dynamical systems. Phys Lett A 104:239–244

    Article  MathSciNet  Google Scholar 

  6. Brunetti C (1939) The transitron oscillator. Proc IRE 27(2):88–94

    Article  Google Scholar 

  7. Chen G, Ueta T (2002) Chaos in circuits and systems. World Scientific, Singapore

    MATH  Google Scholar 

  8. Chua LO (1994) Chua’s circuit 10 year later. Int J Bifurc Chaos 22:279–305

    Google Scholar 

  9. Chua LO, Yu J, Yu Y (1983) Negative resistance devices. Int J Circuit Theory Appl 11:161–186

    Article  MATH  Google Scholar 

  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):732–744

    Google Scholar 

  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):745–761

    Google Scholar 

  12. Cruz JM, Chua LO (1992) A CMOS IC nonlinear resistor for Chua’s circuit. ERL Memorandum, Electronics Research Laboratory, University of California, Berkeley

    Google Scholar 

  13. Dawson P, Grebogi C, Yorke J, Kan I (1992) Antimonotonicity-inevitable reversal of period doubling cascades. Phys Lett A 162:249–252

    Article  MathSciNet  Google Scholar 

  14. Esaki L (1958) New phenomenon in narrow germanium p-n junctions. Phys Rev 109(2):603

    Article  Google Scholar 

  15. Field RJ, Györgyi L (1993) Chaos in chemistry and biochemistry. World Scientific Publishing, Singapore

    Book  Google Scholar 

  16. Feigenbaum MJ (1979) The universal metric properties of nonlinear transformations. J Stat Phys 21:669–706

    Article  MathSciNet  MATH  Google Scholar 

  17. Fortuna L, Frasca M, Xibilia MG (2009) Chua’s circuit implementations: yesterday, today and tomorrow. World Scientific, Singapore

    Google Scholar 

  18. Grebogi C, Yorke J (1997) The impact of chaos on science and society. United Nations University Press, Tokyo

    Google Scholar 

  19. Grebogi C, Ott E, Yorke JA (1983) Crises: sudden changes in chaotic attractors and chaotic transients. Phys D 7:181–200

    Article  MathSciNet  MATH  Google Scholar 

  20. Halle K, Chua LO, Anishchenko V, Safonova M (1992) Signal amplification via chaos: experimental evidence. Int J Bifurc Chaos 2:1011–1020

    Article  MATH  Google Scholar 

  21. Hasselblatt B, Katok A (2003) A first course in dynamics: with a panorama of recent developments. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  22. Hull AW (1918) The dynatron: a vacuum tube possessing negative electric resistance. Proc Inst Radio Eng 6(1):5–35

    Google Scholar 

  23. Kennedy MP (1992) Robust op amp realization of Chua’s circuit. Frequenz 46(3–4):66–80

    Google Scholar 

  24. Kocarev L, Halle K, Eckert K, Chua LO (1993) Experimental observations of antimonotonicity in Chua’s circuit. Int J Bifurc Chaos 3:1051–1055

    Article  MATH  Google Scholar 

  25. Kyprianidis IM, Fotiadou ME (2006) Complex dynamics in Chua’s canonical circuit with a cubic nonlinearity. WSEAS Trans Circuits Syst 5:1036–1043

    Google Scholar 

  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 10:1903–1915

    Google Scholar 

  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: 978-3-540-21448-9

    Google Scholar 

  28. Li TY, Yorke JA (1975) Period three implies chaos. Am Math Mon 82(10):985–992

    Article  MathSciNet  MATH  Google Scholar 

  29. Lorenz EN (1963) Deterministic non-periodic flow. J Atmos Sci 20:130–141

    Article  Google Scholar 

  30. Mandelbrot B (1977) The fractal geometry of nature. W.H. Freeman Company, New York

    MATH  Google Scholar 

  31. Matsumoto T (1984) A chaotic attractor from Chua’s circuit. IEEE Trans Circuits Syst CAS–31(12):1055–1058

    Article  MATH  Google Scholar 

  32. Matsumoto T, Chua LO, Tokumasu K (1986) Double scroll via a two-transistor circuit. IEEE Trans Circuits Syst 33(8):828–835

    Article  MathSciNet  Google Scholar 

  33. May RM (1976) Theoretical ecology: principles and applications. W.B. Saunders Company, Philadelphia

    Google Scholar 

  34. Moon FC (1987) Chaotic vibrations: an introduction for applied scientists and engineers. Wiley, New York

    MATH  Google Scholar 

  35. Nicolis G (1995) Introduction to nonlinear science. Cambridge University Press, Cambridge

    Book  Google Scholar 

  36. Ott E (1993) Chaos in dynamical systems. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  37. Pivka L, Spany V (1993) Boundary surfaces and basin bifurcations in Chua’s circuit. J Circuits Syst Comput 3:441–470

    Article  MathSciNet  Google Scholar 

  38. Poincaré JH (1890) Sur le probleme des trois corps et les equations de la dynamique. Divergence des series de M. Lindstedt. Acta Math 13:1–270

    Google Scholar 

  39. Rössler OE (1976) An equation for continuous chaos. Phys Lett 57A(5):397–398

    Article  Google Scholar 

  40. Strogatz SH (1994) Nonlinear dynamics and chaos. Addison-Wesley, New York

    Google Scholar 

  41. Turner LB (1920) The Kallirotron. An aperiodic negative-resitance triode combination. Radio Rev 1:317–329

    Google Scholar 

  42. Voelcker J (1989) The Gunn effect. IEEE Spectr 26(7). doi:10.1109/6.29344

    Google Scholar 

  43. Zhong GQ, Ayron F (1985) Experimental confirmation of chaos from Chua’s circuit. Int J Circuit Theory Appl 13(11):93–98

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ch. K. Volos .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Giakoumis, A.E., Volos, C.K., Stouboulos, I.N., Kyprianidis, I.M., Nistazakis, H.E., Tombras, G.S. (2016). Implementation of a Laboratory-Based Educational Tool for Teaching Nonlinear Circuits and Chaos. In: Vaidyanathan, S., Volos, C. (eds) Advances and Applications in Chaotic Systems . Studies in Computational Intelligence, vol 636. Springer, Cham. https://doi.org/10.1007/978-3-319-30279-9_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30279-9_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30278-2

  • Online ISBN: 978-3-319-30279-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics