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.

翻译：本文研究一类称为混合基因调控网络（HGRNs）的混合动力系统，该系统被提出用于建模基因调控网络。在HGRNs中，存在可达到固定点或收敛到极限环的良性轨迹，以及表现出非周期或非确定性行为的混沌轨迹。本文研究了HGRNs的这些不规则行为，并提出了关于可达性问题的可判定性、HGRNs非确定性行为的概率以及特别是二维HGRNs中混沌现象的理论结果。