Bistability of Sequestration Networks

TL;DR

This paper proves the existence of multiple steady states and bistability in sequestration networks, demonstrating conditions under which these networks exhibit complex dynamic behavior.

Contribution

It establishes the presence of three positive steady states and bistability in sequestration networks for any odd number of species, advancing understanding of their dynamic properties.

Findings

Three nondegenerate positive steady states exist for these networks.

Two of the steady states are locally asymptotically stable.

Bistability occurs within a non-empty open set in the parameter space.

Abstract

We solve a conjecture on multiple nondegenerate steady states, and prove bistability for sequestration networks. More specifically, we prove that for any odd number of species, and for any production factor, the fully open extension of a sequestration network admits three nondegenerate positive steady states, two of which are locally asymptotically stable. In addition, we provide a non-empty open set in the parameter space where a sequestration network admits bistability.