Stability of bifurcation delay in a delay differential equation with time delay image Original Research Article

In a previous paper [R. Miyazaki, K. Tchizawa, Bifurcation delay in a delay differential equation, Nonlinear Analysis 63 (2005) e2189–e2195], the influence of the delay feedback on the bifurcation delay was discussed. However, the result of numerical experiments is not completely consistent with the theory. In this paper, the structure which was given by numerical experiments was described. The theory on the structure is based on fundamental theorems of the differential-difference equations. The delay feed back made bifurcation delay shorter. We also showed a new result on the stability of bifurcation delay with delay time 2nπ