Networks of coupled circuits: From a versatile toggle switch to collective coherent behavior

We study the versatile performance of networks of coupled circuits. Each of these circuits is composed of a positive and a negative feedback loop in a motif that is frequently found in genetic and neural networks. When two of these circuits are coupled with mutual repression, the system can function as a toggle switch. The variety of its states can be controlled by two parameters as we demonstrate by a detailed bifurcation analy-sis. In the bistable regimes switches between the coexisting attractors can be induced by noise. When we couple larger sets of these units, we numerically observe collective coherent modes of individual fixed-point and limit-cycle behavior. It is there the monotonic change of a single bifurcation parameter that allows to control the onset and arrest of the synchronized oscillations. This mechanism may play a role in biologi-cal applications, in particular in connection with the segmentation clock. While tuning the bifurcation parameter, also a variety of transient pat