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 via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz M, Stegun IA (1968) Handbook of Mathematical Functions, 7th edn. Dover, New York
Bennett WR (1933) New results in the calculation of modulation products. Bell System Techn J 12:228–243
Bernstein SN (1922) Sur l’ordre de la meilleure approximation des functions continues par des polynomes. Mem Acad Royal Belg Sc 2(IV):1–103
de Boer E (1991) Auditory physics. Physical principles in hearing theory. III. Physics Reports 203(3):125–231
Broer HW, Takens F (2009) Dynamical Systems and Chaos. Springer, New York
Davenport WB, Root WL (1958) Random Signals and Noise. McGraw-Hill, New York
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 395–403
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
Feuerstein E (1957) Intermodulation products for ν-law biased wave rectifiers for multiple frequency input. Quart Appl Math pp 183–192
Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer-Verlag, New York
Middleton D (1948) Some general results in the theory of noise through non-linear devices. Quart Appl Math 5:445–498
Middleton D (1960) An Introduction to Statistical Communication Theory. McGraw-Hill, New York
Nayfeh AH, Mook DT (1979) Nonlinear Oscillations. Wiley, New York
van der Pol B (1934) The nonlinear theory of electric oscillations. Proc I R E 22:1051–1086
Rice SO (1945) Mathematical analysis of random noise. IV. Noise through non-linear devices. Bell System Techn J 24:115–162
Sternberg RL, Kaufman H (1953) A general solution of the two-frequency modulation product problem. I. J Math Phys 32:233–242
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 8:457–467
Stoker JJ (1950) Nonlinear Vibrations. Interscience Publishers (later: Wiley), New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Duifhuis, H. (2012). Nonlinear Tools. In: Cochlear Mechanics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6117-4_9
Download citation
DOI: https://doi.org/10.1007/978-1-4419-6117-4_9
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-6116-7
Online ISBN: 978-1-4419-6117-4
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)