On Hybrid Gene Regulatory Networks

In this work, we study a class of hybrid dynamical systems called hybrid gene regulatory networks (HGRNs) which was proposed to model gene regulatory networks. In HGRNs, there exist well-behaved trajectories that reach a fixed point or converge to a limit cycle, as well as chaotic trajectories that behave non-periodic or indeterministic. In our work, we investigate these irregular behaviors of HGRNs and present theoretical results about the decidability of the reachability problem, the probability of indeterministic behavior of HGRNs, and chaos especially in 2-dimensional HGRNs.