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To give a brief historical background.

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Bibliography

  1. A. Agarwal and N. Ananthkrishnan, Bifurcation analysis for onset and cessation of surge in axial flow compressors, International Journal of Turbo & Jet Engines, 17(3) (2000), 207–217.

    Google Scholar 

  2. G. Bella, Multiple cycles and the Bautin bifurcation in the Goodwin model of a class struggle, Nonlinear Analysis: Modelling and Control, 18(3), (2013), 265–274.

    Google Scholar 

  3. R. Fitzhugh, Impulses and physiological states in theoretical models of nerve membranes, J. Biophys., 1182 (1961), 445–466.

    Google Scholar 

  4. E.J. Hinch, Perturbation Methods, Cambridge University Press, 2002.

    Google Scholar 

  5. A.L. Hodgkin and A.F. Huxley, A qualitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117 (1952), 500–544. Reproduced in Bull. Math. Biol. 52 (1990) 25–71.

    Google Scholar 

  6. A. Liénard, Étude des oscillations entrenues, Revue Génerale de Électricité, 23 (1928), 946–954.

    Google Scholar 

  7. Han Mao’an, Bifurcation Theory of Limit Cycles, Alpha Science International Limited, Oxford, 2016.

    Google Scholar 

  8. J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating 1214-nerve axons, Proc. IRL, 50 (1970), 2061–2070.

    Google Scholar 

  9. A.H. Nayfeh, Perturbation Methods, Wiley-Interscience, 2000.

    Google Scholar 

  10. J.C. Neu, Singular Perturbation in the Physical Sciences (Graduate Studies in Mathematics), American Mathematical Society, Rhode Island, 2015.

    Google Scholar 

  11. D.B. Owens, F.J. Capone, R.M. Hall, J.M. Brandon and J.R. Chambers, Transonic free-to-roll analysis of abrupt wing stall on military aircraft, Journal of Aircraft, 41(3) (2004), 474–484.

    Google Scholar 

  12. M.S. Padin, F.I. Robbio, J.L. Moiola and G.R. Chen, On limit cycle approximations in the van der Pol oscillator, Chaos, Solitons and Fractals, 23 (2005), 207–220.

    Google Scholar 

  13. L. Perko, Differential Equations and Dynamical Systems, 3rd ed., Springer-Verlag, Berlin, New York, Heidelberg, 2006.

    Google Scholar 

  14. J. Rayleigh, The Theory of Sound, Dover, New York, 1945.

    Google Scholar 

  15. C. Rocsoreanu, A. Georgeson and N. Giurgiteanu, The Fitzhugh-Nagumo Model: Bifurcation and Dynamics, Kluwer, Dordrecht, Netherlands, 2000.

    Google Scholar 

  16. B. Shivamoggi, Perturbation Methods for Differential Equations, Birkhäuser, Boston, 2006.

    Google Scholar 

  17. B. van der Pol, On relaxation oscillations, Philos. Magazine 7 (1926), 901–912, 946–954.

    Google Scholar 

  18. Ye Yan Qian, Theory of Limit Cycles, Translations of Mathematical Monographs, 66, American Mathematical Society, Rhode Island, 1986.

    Google Scholar 

  19. J.A. Yorke (Contributor), K. Alligood (Ed.), and T. Sauer (Ed.), Chaos: An Introduction to Dynamical Systems, Springer-Verlag, New York, 1996.

    Google Scholar 

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Correspondence to Stephen Lynch .

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Lynch, S. (2017). Limit Cycles. In: Dynamical Systems with Applications Using Mathematica®. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-61485-4_5

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