Qualitative control strategies for synchronization of bistable gene regulatory networks

In this paper we investigate the emergent dynamics in a network of N coupled cells, each expressing a similar genetic bistable switch. The bistable switch is modeled as a piecewise affine system and the cells are diffusively coupled. We show that both the coupling topology and the strength of the diffusion parameter may introduce new steady state patterns in the network. We study the synchronization properties of the coupled network and, using a control set of only three possible values (u min , u max , or 1), propose different control strategies which stabilize the system into a chosen synchronization pattern , both in the weak and strong coupling regimes. The results are illustrated by several numerical examples.