Monotone chemical reaction networks
نویسندگان
چکیده
We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion effects are taken into account, the conclusions remain unchanged. The main tools used in our analysis come from the theory of monotone dynamical systems. We review some of the features of this theory and provide a selfcontained proof of a particular attractivity result which is used in proving our main result.
منابع مشابه
A tutorial on monotone systems- with an application to chemical reaction networks
Monotone systems are dynamical systems for which the flow preserves a partial order. Some applications will be briefly reviewed in this paper. Much of the appeal of the class of monotone systems stems from the fact that roughly, most solutions converge to the set of equilibria. However, this usually requires a stronger monotonicity property which is not always satisfied or easy to check in appl...
متن کاملGraph-theoretic Analysis of Multistability and Monotonicity for Biochemical Reaction Networks
Mathematical models of biochemical reaction networks are usually high dimensional, nonlinear, and have many unknown parameters, such as reaction rate constants, or unspecified types of chemical kinetics (such as mass-action, Michaelis-Menten, or Hill kinetics). On the other hand, important properties of these dynamical systems are often determined by the network structure, and do not depend on ...
متن کاملPhase-translation group actions on strongly monotone skew-product semiflows
We establish a convergence property for pseudo-bounded forward orbits of strongly monotone skew-product semiflows with invariant phase-translation group actions. The results are then applied to obtain global convergence of certain chemical reaction networks whose induced systems in reaction coordinates are monotone, as well as the dynamics of certain reaction-diffusion systems, in time-recurren...
متن کاملSensitivity of chemical reaction networks : a structural approach . 2 . Regular monomolecular systems
For the deceptively innocent case of monomolecular reactions, only, we embark on a systematic mathematical analysis of the steady state response to perturbations of reaction rates. Our structural sensitivity analysis is based on the directed graph structure of the monomolecular reaction network, only. In fact, our function-free approach does not require numerical input. We work with general, no...
متن کاملGraph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates.
This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it investigates their monotonicity and convergence under the assumption that the rates of the reactions are monotone functions of the concentrations of their reactants. This is satisfied for, yet not restricted to, the most common choices of the reaction k...
متن کامل