Coexistence of multi-attractor in small genetic regulatory networks

摘要

The dynamics of living things are obviously complicated. Genetic regulatory networks of organisms have the capacity to show various attractor phenotypes. This paper focus on the coexistence of multiple types of attractors in a simple tri-node genetic motif. We discuss the coexistence of multiple equilibriums for the genetic motif and establish the stability criteria for each equilibrium. The dynamic display of the genetic motif depends on different biochemical parameters and initial conditions. It is proved that the motif at least exists a point attractor for sure, and the point attractor is so special that it is also a structure switching attractor. The topology of the tri-node motif will change into a two-node negative feedback loop under right initial conditions. Besides, the motif may also have other types of attractors (periodic and chaotic attractors) under some biochemical parameters. Several numerical simulations are illustrated to deepen our insight.