Universal bifurcation scenarios in delay-differential equations with one delay (Q6595386)

The authors are concerned with studying bifurcation scenarios for ordinary delay differential equations. They study how time-delay affects the stability of equilibria. When the time-delay is varied, although the equilibrium of the DDE remains unchanged, its stability may change. This paper builds on recent work that provided necessary and sufficient conditions for DDEs with multiple delays to have delay-independent stability. The authors show that DDEs that are not absolutely stable exhibit sequences of stabilization or destabilization bifurcations as the time-delay changes. They show that DDEs with a single delay have only a limited number of possible bifurcation scenarios. Thus the paper introduces so-called universality classes of linear DDEs, such that within each universality class each DDE has the same behaviour of the critical eigenvalues.