Reachability, persistence, and constructive chemical reaction networks (part II): a formalism for species composition in chemical reaction network theory and application to persistence

2011 ◽  
Vol 49 (10) ◽  
pp. 2137-2157 ◽  
Author(s):  
Gilles Gnacadja
Keyword(s):  
Species Composition ◽  
Chemical Reaction ◽  
Network Theory ◽  
Reaction Network ◽  
Chemical Reaction Networks ◽  
Chemical Reaction Network ◽  
Reaction Networks ◽  
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 Early warning signals in chemical reaction networks

2020 ◽  
Vol 56 (26) ◽  
pp. 3725-3728
Author(s):  
Oliver R. Maguire ◽  
Albert S. Y. Wong ◽  
Jan Harm Westerdiep ◽  
Wilhelm T. S. Huck
Keyword(s):  
Complex Systems ◽  
Chemical Reaction ◽  
Early Warning ◽  
Reaction Network ◽  
Chemical Reaction Networks ◽  
Chemical Reaction Network ◽  
Reaction Networks ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Complex Chemical

Many natural and man-made complex systems display early warning signals when close to an abrupt shift in behaviour. Here we show that such early warning signals appear in a complex chemical reaction network.

Inference of Chemical Reaction Networks Using Hybrid S-system Models

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Dominic P Searson ◽  
Mark J Willis ◽  
Simon J Horne ◽  
Allen R Wright
Keyword(s):  
Chemical Reaction ◽  
Power Law ◽  
Network Inference ◽  
Batch Reactor ◽  
Reaction Network ◽  
Chemical Reaction Networks ◽  
Chemical Reaction Network ◽  
Reaction Networks ◽  
Fed Batch ◽  
System Equations

This article demonstrates, using simulations, the potential of the S-system formalism for the inference of unknown chemical reaction networks from simple experimental data, such as that typically obtained from laboratory scale reaction vessels. Virtually no prior knowledge of the products and reactants is assumed. S-systems are a power law formalism for the canonical approximate representation of dynamic non-linear systems. This formalism has the useful property that the structure of a network is dictated only by the values of the power law parameters. This means that network inference problems (e.g. inference of the topology of a chemical reaction network) can be recast as parameter estimation problems. The use of S-systems for network inference from data has been reported in a number of biological fields, including metabolic pathway analysis and the inference of gene regulatory networks. Here, the methodology is adapted for use as a hybrid modelling tool to facilitate the reverse engineering of chemical reaction networks using time series concentration data from fed-batch reactor experiments. The principle of the approach is demonstrated with noisy simulated data from fed-batch reactor experiments using a hypothetical reaction network comprising 5 chemical species involved in 4 parallel reactions. A co-evolutionary algorithm is employed to evolve the structure and the parameter values of the S-system equations concurrently. The S-system equations are then interpreted in order to construct a network diagram that accurately reflects the underlying chemical reaction network.

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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