An algorithm for detecting small solutions for delay differential equations

This talk begins by introducing delay differential equations and (in particular) the need to detect small solutions. We discuss how small solutions influence the behaviour and analysis of solutions of the underlying equation and explain why they are difficult to detect. Next the talk focuses on a methodology that can be proved to show the existence of small solutions for certain linear equations and we show how the method can be automated using a computer. The talk concludes with examples of how the automated system can detect small solutions in the equations, and details of how the method can be extended to a wider class of equations.