Delay differential equations : detection of small solutions
This thesis concerns the development of a method for the detection of small solutions to delay differential equations. The detection of small solutions is important because their presence has significant influence on the analytical prop¬erties of an equation. However, to date, analytical methods are of only limited practical use. Therefore this thesis focuses on the development of a reliable new method, based on finite order approximations of the underlying infinite dimen¬sional problem, which can detect small solutions. Decisions (concerning the existence, or otherwise, of small solutions) based on our visualisation technique require an understanding of the underlying methodol¬ogy behind our approach. Removing this need would be attractive. The method we have developed can be automated, and at the end of the thesis we present a prototype Matlab code for the automatic detection of small solutions to delay differential equations.