Foundations of Chemical Reaction Network Theory

2019 ◽  
Author(s):  
Martin Feinberg
Keyword(s):  
Chemical Reaction ◽  
Network Theory ◽  
Reaction Network ◽  
Chemical Reaction Network ◽  
Chemical Reaction Network Theory

Using chemical reaction network theory to discard a kinetic mechanism hypothesis

2005 ◽  
Vol 152 (4) ◽  
pp. 243 ◽  
Author(s):  
C. Conradi ◽  
J. Saez-Rodriguez ◽  
E.-D. Gilles ◽  
J. Raisch
Keyword(s):  
Chemical Reaction ◽  
Network Theory ◽  
Reaction Network ◽  
Kinetic Mechanism ◽  
Chemical Reaction Network ◽  
Chemical Reaction Network Theory

scholarly journals An algorithm for building and integrating dynamic systems based on reaction networks

2021 ◽  
Vol 8 (1) ◽  
pp. 49
Author(s):  
Petar Chernev
Keyword(s):  
Chemical Reaction ◽  
Dynamic Systems ◽  
Network Theory ◽  
Dynamic Models ◽  
Reaction Network ◽  
Chemical Reaction Network ◽  
Reaction Networks ◽  
Complex Interactions ◽  
Model Complex ◽  
Chemical Reaction Network Theory

In the present work we give an overview and implementation of an algorithm for building and integrating dynamic systems from reaction networks. Reaction networks have their roots in chemical reaction network theory, but their nature is general enough that they can be applied in many fields to model complex interactions. Our aim is to provide a simple to use program that allows for quick prototyping of dynamic models based on a system of reactions. After introducing the concept of a reaction and a reaction network in a general way, not necessarily connected to chemistry, we outlay the algorithm for building its associated system of ODEs. Finally, we give a few example usages where we examine a range of growth-decay models in the context of reaction networks.

scholarly journals Using chemical reaction network theory to show stability of distributional dynamics in game theory

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ross Cressman ◽  
Vlastimil Křivan
Keyword(s):  
Game Theory ◽  
Chemical Reaction ◽  
Network Theory ◽  
Group Formation ◽  
Evolutionary Game ◽  
Reaction Network ◽  
Chemical Reaction Network ◽  
Positive Equilibrium ◽  
Distributional Dynamics ◽  
Chemical Reaction Network Theory

<p style='text-indent:20px;'>This article shows how to apply results of chemical reaction network theory (CRNT) to prove uniqueness and stability of a positive equilibrium for pairs/groups distributional dynamics that arise in game theoretic models. Evolutionary game theory assumes that individuals accrue their fitness through interactions with other individuals. When there are two or more different strategies in the population, this theory assumes that pairs (groups) are formed instantaneously and randomly so that the corresponding pairs (groups) distribution is described by the Hardy–Weinberg (binomial) distribution. If interactions times are phenotype dependent the Hardy-Weinberg distribution does not apply. Even if it becomes impossible to calculate the pairs/groups distribution analytically we show that CRNT is a general tool that is very useful to prove not only existence of the equilibrium, but also its stability. In this article, we apply CRNT to pair formation model that arises in two player games (e.g., Hawk-Dove, Prisoner's Dilemma game), to group formation that arises, e.g., in Public Goods Game, and to distribution of a single population in patchy environments. We also show by generalizing the Battle of the Sexes game that the methodology does not always apply.</p>

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