相关论文: A survey of methods for deciding whether a reactio…
Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. Bistable reaction networks are posited to underlie biochemical switches, which motivates the…
We characterize completely the capacity for (nondegenerate) multistationarity of mass action reaction networks with one-dimensional stoichiometric subspace in terms of reaction structure. Specifically, we show that networks with two or more…
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…
We study the multistationarity for the reaction networks with one-dimensional stoichiometric subspaces, and we focus on the networks admitting finitely many positive steady states. We prove that if a network admits multistationarity, then…
Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we…
Much attention has been focused in recent years on the following algebraic problem arising from applications: which chemical reaction networks, when taken with mass-action kinetics, admit multiple positive steady states? The interest behind…
Biochemical models that exhibit bistability are of interest to biologists and mathematicians alike. Chemical reaction network theory can provide sufficient conditions for the existence of bistability, and on the other hand can rule out the…
This article characterizes certain small multistationary chemical reaction networks. We consider the set of fully open networks, those for which all chemical species participate in inflow and outflow, containing one non-flow (reversible or…
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…
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…
Zero-one biochemical reaction networks play key roles in cell signalling such as signalling pathways regulated by protein phosphorylation. Multistability of reaction networks is a crucial dynamics feature enabling decision-making in cells.…
This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon the existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we…
The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on…
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…
We consider a natural class of reaction networks which consist of reactions where either two species can inactivate each other (i.e., sequestration), or some species can be transformed into another (i.e., transmutation), in a way that gives…
Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems, and can be used in other contexts such as in systems biology to study cellular signaling pathways or epidemiology to study the…
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…
We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows…
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,…
For the reaction networks with one-dimensional stoichiometric subspaces, we show the following results. (1) If the maximum number of positive steady states is an even number N, then the maximum number of stable positive steady states is…