Nonlinear Tools

Chapter
First Online:

Abstract

This chapter presents tools that are available for the analysis of nonlinear properties of (some of the constituents of) the cochlea. It starts with a reference to properties of power law devices. In the next section it discusses properties of nonlinear oscillators in more detail than was done in Chap. 5.

This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramowitz M, Stegun IA (1968) Handbook of Mathematical Functions, 7th edn. Dover, New YorkGoogle Scholar
  2. Bennett WR (1933) New results in the calculation of modulation products. Bell System Techn J 12:228–243Google Scholar
  3. Bernstein SN (1922) Sur l’ordre de la meilleure approximation des functions continues par des polynomes. Mem Acad Royal Belg Sc 2(IV):1–103Google Scholar
  4. de Boer E (1991) Auditory physics. Physical principles in hearing theory. III. Physics Reports 203(3):125–231Google Scholar
  5. Broer HW, Takens F (2009) Dynamical Systems and Chaos. Springer, New YorkGoogle Scholar
  6. Davenport WB, Root WL (1958) Random Signals and Noise. McGraw-Hill, New YorkGoogle Scholar
  7. Duifhuis H (1989) Power-law nonlinearities: A review of some less familiar properties. In: Wilson JP, Kemp DT (eds) Cochlear Mechanisms: Structure, Function and Models, Plenum, New York, pp 395–403Google Scholar
  8. EOMlist (2002) Differential equation, ordinary. E.F. Mishchenko (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Differential_equation,_ordinary&oldid=13954
  9. Feuerstein E (1957) Intermodulation products for ν-law biased wave rectifiers for multiple frequency input. Quart Appl Math pp 183–192Google Scholar
  10. Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer-Verlag, New YorkGoogle Scholar
  11. Middleton D (1948) Some general results in the theory of noise through non-linear devices. Quart Appl Math 5:445–498Google Scholar
  12. Middleton D (1960) An Introduction to Statistical Communication Theory. McGraw-Hill, New YorkGoogle Scholar
  13. Nayfeh AH, Mook DT (1979) Nonlinear Oscillations. Wiley, New YorkGoogle Scholar
  14. van der Pol B (1934) The nonlinear theory of electric oscillations. Proc I R E 22:1051–1086CrossRefGoogle Scholar
  15. Rice SO (1945) Mathematical analysis of random noise. IV. Noise through non-linear devices. Bell System Techn J 24:115–162Google Scholar
  16. Sternberg RL, Kaufman H (1953) A general solution of the two-frequency modulation product problem. I. J Math Phys 32:233–242Google Scholar
  17. Sternberg RL, Shipman JS, Kaufman H (1955) Tables of bennett functions for the two-frequency modulation product problem for the half-wave linear rectifier. Quart J Appl Math 8:457–467CrossRefGoogle Scholar
  18. Stoker JJ (1950) Nonlinear Vibrations. Interscience Publishers (later: Wiley), New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics and Natural SciencesUniversity of GroningenGroningenThe Netherlands
  2. 2.BCN-NeuroImaging CenterGroningenThe Netherlands

Personalised recommendations