Delay as Bifurcation Parameter

Abstract

It is well-known that the equilibrium positions of dynamical systems are usually destabilized by increasing delay. However, opposite effects can also be experienced in special cases. In practice such situations may occur in some models of population dynamics, in the case of machine tool vibrations, in controls of manipulators or in man-machine systems. The equilibrium of such a system may get back its stability if the delay is great enough in spite of the fact that it loses its stability at a small value of the time lag. Thus, it is interesting to investigate these problems from the point of view of Hopf bifurcations because the trivial solutions may have a lot of bifurcation points with respect to the delay.