Minimal invariant regions and minimal globally attracting regions for variable-k reaction systems

2021/10/27 by Yida Ding, Ding, Yida, Abhishek Deshpande +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #14M25 #37N25 #80A30 #92C45 #92E20 #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.2110.14486

openalex publication_date 2021/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The structure of invariant regions and globally attracting regions is fundamental to understanding the dynamical properties of reaction network models. We describe an explicit construction of the minimal invariant regions and minimal globally attracting regions for dynamical systems consisting of two reversible reactions, where the rate constants are allowed to vary in time within a bounded interval.

Citations

• Toric Differential Inclusions and a Proof of the Global Attractor\n Conjecture

Related

• Realizations through Weakly Reversible Networks and the Globally Attracting Locus
• The dynamics of weakly reversible population processes near facets
• A proof of the Global Attractor Conjecture in the single linkage class case
• Boundedness of trajectories for weakly reversible, single linkage class reaction systems
• Attainable Regions of Dynamical Systems