 The time-delayed Pyrogas control scheme applied to the dissipative Dickey model via modulation of the atom field coupling creates an infinite sequence of non-equilibrium phases with fixed points and limit cycles in the primary super-radiant regime, which we analyze as a hopf bifurcation scenario and determine analytical conditions for phase boundaries. This article was authored by Vasiliy Copilov, Clive Emery, Eckhart Scholl, and others.