STABILITY AND BIFURCATIONS OF EQUILIBRIA IN A MULTIPLE-DELAYED DIFFERENTIAL-EQUATION

The influence of multiple negative delayed feedback loops on the stabi lity of a single-action mechanism are considered. A characteristic equ ation for the linearized stability of the equilibrium is completely an alyzed, as a function of two parameters describing a delay in one loop and a ratio of the gains in the two feedback loops. The bifurcations occurring as the linear stability is lost are analyzed by the construc tion of a centre manifold. In particular, the nature of Hopf and more degenerate, higher codimension bifurcations are explicitly determined.