Dynamic Nonlinear Networks

  • Bharathwaj Muthuswamy
  • Santo Banerjee


We will now learn about techniques for analyzing dynamic circuits, that are governed by differential equations. We will emphasize fundamental concepts behind dynamic nonlinear networks, time domain analysis of nth-order nonlinear networks, frequency response concepts, circuit analysis techniques for memristive networks and energy approaches (Lagrangian, Hamiltonian). We cannot hope to cover all the analysis techniques for dynamic nonlinear networks in detail in one chapter. Nevertheless, this chapter should prepare the reader for picking up advanced techniques for analyzing dynamic nonlinear networks from any specialized references.


  1. 1.
    Ambelang, S., Muthuswamy, B.: From Van der Pol to Chua: an introduction to nonlinear dynamics and chaos for second year undergraduates. In: Proceedings of the 2012 IEEE International Symposium on Circuits and Systems, pp. 2937–2940 (2012)Google Scholar
  2. 2.
    Calaprice, A. (ed.): The Ultimate Quotable Einstein. Princeton University Press/The Hebrew University of Jerusalem, Princeton/Jerusalem (2011)zbMATHGoogle Scholar
  3. 3.
    Chua, L.O.: Introduction to Nonlinear Network Theory. McGraw-Hill, New York (1969)Google Scholar
  4. 4.
    Chua, L.O.: Memristor - the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)CrossRefGoogle Scholar
  5. 5.
    Chua, L.O.: Device modeling via basic nonlinear circuit elements. IEEE Trans. Circuits Syst. 27(11), 1014–1044 (1980)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chua, L.O.: Dynamic nonlinear networks: state-of-the-art. IEEE Trans. Circuits Syst. 27(11), 1059–1087 (1980)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Chua, L.O.: Nonlinear circuit foundations for nanodevices, part I: the four-element torus (invited paper). Proc. IEEE 91(11), 1830–1859 (2003)CrossRefGoogle Scholar
  8. 8.
    Chua, L.O.: Supplementary Lecture Notes on First-Order Circuits. University of California, Berkeley (Fall 2008), pp. EE100. Available, online: Accessed 29 Dec 2017
  9. 9.
    Chua, L.O., Kang, S.M.: Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Chua, L.O., Szeto, E.W.: Synthesis of higher order nonlinear circuit elements. IEEE Trans. Circuits Syst. 31(2), 231–235 (1984)CrossRefGoogle Scholar
  11. 11.
    Chua, L.O., Tseng, C.: A Memristive circuit model for pn junction diodes. Int. J. Circuit Theory Appl. 4(2), 367–389 (1976)Google Scholar
  12. 12.
    Chua, L.O., Desoer, C.A., Kuh, E.S.: Linear and Nonlinear Circuits. McGraw-Hill, New York (1987)zbMATHGoogle Scholar
  13. 13.
    Corinto, F., Forti, M.: Memristor circuits: flux-charge analysis method. IEEE Trans. Circuits Syst. Regul. Pap. 63(11), 1997–2009 (2016)CrossRefGoogle Scholar
  14. 14.
    Desoer, C.A., Kuh, E.S.: Basic Circuit Theory. Tata McGraw Hill, New York (1969)Google Scholar
  15. 15.
    Elwakil, A.S., Kennedy, M.P.: Chaotic oscillator configuration using a frequency dependent negative resistor. J. Circuits Syst. Comput. 9(3,4), 229–242 (1999)CrossRefGoogle Scholar
  16. 16.
    Georgiou, P.S., et al.: On Memristor ideality and reciprocity. Microelectron. J. 45(11), 1363–1371 (2014)CrossRefGoogle Scholar
  17. 17.
    Hamill, P.: A Student’s Guide to Lagrangians and Hamiltonians. Cambridge University Press, Cambridge (2013)CrossRefGoogle Scholar
  18. 18.
    Havil, J.: Gamma : Exploring Euler’s Constant. Princeton University Press, Princeton (2003)zbMATHGoogle Scholar
  19. 19.
    Jeltsema, D., Scherpen, J.M.A.: Multidomain modeling of nonlinear networks and systems. IEEE Control. Syst. 29(4), 28–59 (2009)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Kennedy, M.P., Chua, L.O.: Hysteresis in electronic circuits: a circuit theorist’s perspective. Int. J. Circuit Theory Appl. 19, 471–515 (1991)CrossRefGoogle Scholar
  21. 21.
    Lin, D., Hui, S.Y.R., Chua, L.O.: Gas discharge lamps are volatile memristors. IEEE Trans. Circuits Syst. Regul. Pap. 61(7), 2066–2073 (2014)CrossRefGoogle Scholar
  22. 22.
    Marszalek, W.: On the action parameter and one-period loops of oscillatory memristive circuits. Nonlinear Dyn. 82(1–2), 619–628 (2015)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Muthuswamy, B., Chua, L.O.: Simplest chaotic circuit. Int. J. Bifurcation Chaos 20(5), 1567–1680 (2010)CrossRefGoogle Scholar
  24. 24.
    Muthuswamy, B., et al.: Memristor modelling. In: Proceedings of the 2014 IEEE ISCAS, pp. 490–493 (2014)Google Scholar
  25. 25.
    Needham, T.: Visual Complex Analysis. Oxford University Press, Oxford (2000)zbMATHGoogle Scholar
  26. 26.
    Penfield, P.P.: Varactor Applications, p. 513. M.I.T. Press, Cambridge (1962). Available, online:
  27. 27.
    Riaza, R., Tischendorf, C.: Semistate models of electrical circuits including memristors. Int. J. Circuit Theory Appl. 39(6), 607–627 (2011)CrossRefGoogle Scholar
  28. 28.
    Sah, M.P., et al.: A generic model of memristors with parasitic components. IEEE Trans. Circuits Syst. Regul. Pap. 62(3), 891–898 (2015)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Weisstein, E.W.: Second Fundamental Theorem of Calculus (2018). Available, online: Accessed 1 Jan 2018

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Bharathwaj Muthuswamy
    • 1
  • Santo Banerjee
    • 2
  1. 1.Department of Physics, QuEST LabStevens Institute of TechnologyHobokenUSA
  2. 2.Institute for Mathematical ResearchUniversity Putra MalaysiaSerdangMalaysia

Personalised recommendations