Related papers: Multistability of Reaction Networks with One-Dimen…
This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect…
Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling…
Multistationary chemical reaction networks are of interest to scientists and mathematicians alike. While some criteria for multistationarity exist, obtaining explicit reaction rates and steady states that exhibit multistationarity for a…
Stochastic reaction networks (SRNs) provide models of many real-world networks. Examples include networks in epidemiology, pharmacology, genetics, ecology, chemistry, and social sciences. Here, we model stochastic reaction networks by…
In Systems Biology there is a growing interest in the question, whether or not a given mathematical model can admit more than one steady state. As parameter values are often unknown or subject to a very high uncertainty, one is often…
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the…
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…
The distributive sequential n-site phosphorylation/dephosphorylation system is an important building block in networks of chemical reactions arising in molecular biology, which has been intensively studied. In the nice paper of Wang and…
Zero-one reaction networks are pivotal to cellular signaling, and establishing the equivalence of such networks represents a foundational computational challenge in the realm of chemical reaction network research. Herein, we propose a…
We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed…
A reaction system exhibits "absolute concentration robustness" (ACR) in some species if the positive steady-state value of that species does not depend on initial conditions. Mathematically, this means that the positive part of the variety…
Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open…
A class of chemical reaction networks is described with the property that each positive equilibrium is locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies. The reaction systems treated…
Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state; while some networks exhibit absolute concentration robustness (ACR), which means that some species…
The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state degree is through the mixed volume of the steady-state system…
Chemical reaction networks taken with mass-action kinetics are dynamical systems that arise in chemical engineering and systems biology. In general, determining whether a chemical reaction network admits multiple steady states is difficult,…
Steady states are frequently used to investigate the long-term behaviors of (bio)-chemical systems. Recently, there has been a growing interest in network-based approaches due to their efficiency in deriving parametrizations of positive…
Given a real sparse polynomial system, we present a general framework to find explicit coefficients for which the system has more than one positive solution, based on the recent article by Bihan, Santos and Spaenlehauer. We apply this…
We analyze the solutions, on single network instances, of a recently introduced class of constraint-satisfaction problems (CSPs), describing feasible steady states of chemical reaction networks. First, we show that the CSPs generalize the…
A multistationarity region is the part of a reaction network's parameter space that gives rise to multiple steady states. Mathematically, this region consists of the positive parameters for which a parametrized family of polynomial…