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. Technical Report: CaltechEERL:1982.DYNL-82-02. California Institute of Technology.

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Abstract

A difference equation with a cubic nonlinearity is examined. Using a phase plane analysis, both quasi-periodic and chaotically behaving solutions am 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.

EPrint Type:	Monograph (Technical Report)
Additional Information:	PhD, 1982
Subjects:	All Records > Dynamics Laboratory
ID Code:	258
Deposited By:	Jim O'Donnell
Deposited On:	14 May 2002
Record Number:	CaltechEERL:1982.DYNL-82-02
Official Persistent URL:	http://resolver.caltech.edu/CaltechEERL:1982.DYNL-82-02
Usage Policy:	You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.

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