Umist How Do Numerical Methods Perform for Delay Diierential Equations Undergoing a Hopf Bifurcation? a Report in Association with Chester College Departments of Mathematics How Do Numerical Methods Perform for Delay Diierential Equations Undergoing a Hopf Bifurcation?

In this paper we consider the numerical solution of delay diierential equations (DDEs) undergoing a Hopf bifurcation. The aim is to understand what will happen when simple standard numerical methods are used to obtain an approximate solution. We present three distinctive and complementary approaches to the analysis which together provide us with the result that # methods applied to a DDE will retain Hopf bifurcations and preserve their type, for suuciently small h > 0.