Bachelor Thesis Oscillation suppression in nonlinear coupled oscillators with and without time delay

The aim of this thesis is to study analytically oscillation death in a system of two coupled Stuart-Landau oscillators. The coupling is chosen to break the rotational symmetry of the single oscillators. We consider both instantaneous and delayed coupling. A detailed bifurcation analysis of the system is done. In the instantaneous case we are able to show that oscillation death always appears if the coupling is strong enough. Explicit values are given. In the delayed case, we show for the first time that oscillation death can occur at all. We find that the region in which oscillation death occurs only varies slightly from the instantaneous case.