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The Analysis of a Nonlinear Difference Equation Occurring in Dynamical Systems


Reinhall, Per Gustaf (1982) The Analysis of a Nonlinear Difference Equation Occurring in Dynamical Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/X17F-E253.


A difference equation with a cubic nonlinearity is examined. Using a phase plane analysis, both quasi-periodic and chaotically behaving solutions are found. The chaotic behavior is investigated in relation to heteroclinic and homoclinic oscillations of stable and unstable solution manifolds emanating from unstable periodic points. Certain criteria are developed which govern the existence of the stochastic behavior. An approximate solution technique is developed giving expressions for the quasi-periodic solutions close to a stable periodic point and the accuracy of these expressions are investigated. The stability of the solutions is examined and approximate local stability criteria are obtained. Stochastic excitation of a nonlinear difference equation is also considered and an approximate value of the second moment of the solution is obtained.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mechanics
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:
  • Knowles, James K. (chair)
  • Miklowitz, Julius
  • Corngold, Noel Robert
  • Cohen, Donald S.
  • Caughey, Thomas Kirk
Defense Date:4 March 1982
Non-Caltech Author Email:reinhall (AT)
Funding AgencyGrant Number
Record Number:CaltechETD:etd-07082005-102658
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2834
Deposited By: Imported from ETD-db
Deposited On:08 Jul 2005
Last Modified:25 Jun 2020 21:02

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