منابع مشابه
Monotone chemical reaction networks
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 a...
متن کاملTranslated chemical reaction networks.
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 of polynomial ordinary differential equations. The steady states of these mass action systems have been analyzed via a variety of techniques, including stoi...
متن کاملConcordant chemical reaction networks.
We describe a large class of chemical reaction networks, those endowed with a subtle structural property called concordance. We show that the class of concordant networks coincides precisely with the class of networks which, when taken with any weakly monotonic kinetics, invariably give rise to kinetic systems that are injective - a quality that, among other things, precludes the possibility of...
متن کاملA 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 کاملNotes on Chemical Reaction Networks
These notes are shamelessly cribbed from the extremely helpful online notes [2]. Even most of the notation is the same. I wrote them because, like Goethe’s Frenchman, I wanted to translate Gunawardena’s notes into my own language. I also benefitted from conversations with Moe Hirsch and Gheorghe Craciun and from lectures by Gheorghe Craciun and David Anderson. 1. Notation. The positive real num...
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ژورنال
عنوان ژورنال: Journal of Mathematical Chemistry
سال: 2006
ISSN: 0259-9791,1572-8897
DOI: 10.1007/s10910-006-9075-z