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On Hybrid Gene Regulatory Networks

Adrian Wurm, Honglu Sun

TL;DR

This work investigates irregular behaviors of HGRNs and presents theoretical results about the decidability of the reachability problem, the probability of indeterministic behavior of HGRNs, and chaos especially in 2-dimensional HGRNs.

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.

On Hybrid Gene Regulatory Networks

TL;DR

This work investigates irregular behaviors of HGRNs and presents theoretical results about the decidability of the reachability problem, the probability of indeterministic behavior of HGRNs, and chaos especially in 2-dimensional HGRNs.

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.
Paper Structure (2 sections, 3 equations)

This paper contains 2 sections, 3 equations.

Table of Contents

  1. Introduction
  2. Preliminaries and Network Reachability Problems

Theorems & Definitions (6)

  • definition thmcounterdefinition: Hybrid gene regulatory network (HGRN)
  • definition thmcounterdefinition: Hybrid state of HGRN
  • definition thmcounterdefinition: Boundary
  • definition thmcounterdefinition: Hybrid trajectory
  • definition thmcounterdefinition: Reachability Problem
  • definition thmcounterdefinition: Area of attraction