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A study of the periodic and quasi-periodic solutions of the discrete duffing equation


Anderson, Mark Carter (1986) A study of the periodic and quasi-periodic solutions of the discrete duffing equation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/RCHW-E496.


The present investigation concentrates on the phenomenological and analytically quantitative study of the periodic and quasi-periodic solutions of a class of conservative, autonomous, nonlinear difference equations. In particular, an equation with a cubic nonlinearity, i.e., a form of the discrete Duffing equation, is studied. Following a simple analysis of the equilibrium solutions, the global structures of the phase portraits are illustrated phenomenologically for different values of the equation parameters. Three discrete perturbation procedures are then developed to obtain a consistent approximation for periodic and quasi- periodic solutions. These approximate solutions contain certain "small divisors" in every term other than the zero'th order term. An examination of the consequences of the vanishing of such a "small divisor" leads to a method of constructing exact periodic solutions in the form of finite Fourier series. The thesis concludes with a discussion of the quasi-periodic approximate solutions and their applicability.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:difference equation, perturbation method, nonlinear system
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Caughey, Thomas Kirk
Thesis Committee:
  • Corngold, Noel Robert
Defense Date:3 October 1985
Non-Caltech Author Email:mcanderson (AT)
Record Number:CaltechETD:etd-03252008-105035
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1121
Deposited By: Imported from ETD-db
Deposited On:04 Apr 2008
Last Modified:21 Dec 2019 02:08

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