Qualitative Behavior Of Dynamical Vector Fields

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Title: Qualitative Behavior Of Dynamical Vector Fields
Author: Kirby, Roger Dale
Abstract: Differential Equations come in two classes , deterministic and stochastic . The first part of this analysis establishes the stable properties of the set of all trajectories converging on a critical point in the real plane defined by two distinct negative eigenvalues . Also in the deterministic class I offer a method for finding closed -form primitives for a great variety of differential forms , through a reduction process facilitated by a Lyapunov -type Energy function . Many of these forms lie in classes which heretofore have not been shown to be solvable in closed form . The last part of this work outlines the appropriate procedures for calculating differentials and solutions for fields perturbed by random processes . In the final chapter a new theory of Laplace Transforms for stochastic calculations has been developed . The introduction of a Table of Transforms has been initiated , and shall eventually be enlarged . Applications are offered to demonstrate its utility .
URI: http : / /hdl .handle .net /10106 /617
Date: 2007-09-17


Qualitative Behavior Of Dynamical Vector Fields. Available electronically from http : / /hdl .handle .net /10106 /617 .

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