相关论文: Positive Steady-State Varieties of Small Chemical …
Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems…
The steady-state degree of a chemical reaction network is the number of complex steady-states, which is a measure of the algebraic complexity of solving the steady-state system. In general, the steady-state degree may be difficult to…
Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…
We establish that mass conserving single terminal-linkage networks of chemical reactions admit positive steady states regardless of network deficiency and the choice of reaction rate constants. This result holds for closed systems without…
We consider steady states of dynamics that have an underlying network structure. We study how a steady state responds to small perturbations in the network parameters and how this sensitivity is connected to the network structure. We…
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…
Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic…
Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…
Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…
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…
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 consider linear elimination of variables in steady state equations of a chemical reaction network. Particular subsets of variables corresponding to sets of so-called reactant-noninteracting species, are introduced. The steady state…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant…
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…
We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we…
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…
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…
We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…
We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well…