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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. California Institute of Technology . (Unpublished) http://resolver.caltech.edu/CaltechEERL:1982.DYNL-82-02

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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.


Item Type:Report or Paper (Technical Report)
Additional Information:PhD, 1982
Group:Dynamics Laboratory
Record Number:CaltechEERL:1982.DYNL-82-02
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.
ID Code:26459
Collection:CaltechEERL
Deposited By: Imported from CaltechEERL
Deposited On:14 May 2002
Last Modified:26 Dec 2012 13:58

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