On Hybrid Gene Regulatory Networks

TL;DR

This paper investigates hybrid gene regulatory networks, analyzing their dynamic behaviors including fixed points, limit cycles, chaos, and the decidability of reachability, providing theoretical insights into their complex dynamics.

Contribution

It offers new theoretical results on the decidability, probability of indeterminism, and chaos in hybrid gene regulatory networks, especially in 2D models.

Findings

Well-behaved trajectories reach fixed points or limit cycles

Chaotic trajectories exhibit non-periodic behavior

Decidability of reachability in HGRNs is established

Abstract

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.