Chemical reactions as dynamical systems on the interval |
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Authors: | L Rondoni R F Streater |
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Institution: | (1) Center for Transport Theory and Mathematical Physics, Virginia Polytechnic Institute, USA;(2) State University, 24061 Blacksburg, Virginia |
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Abstract: | We consider the most general chemical reaction of the typen
1
A
1+...+n
N
A
N
m
1
B
1+...+m
M
B
M
whereN,M 1,n
1,...,n
N
andm
1,...,m
M
are positive integers defining the stoichiometry, andA
1,...,A
N
andB
1,...,B
M
are the names of chemicals or ions. We assume that
i=1
N
ni=
j=1
M
mj. The time evolution of the concentrations is given by the law of mass action and leads to a dynamical system (with discrete or continuous time) which is governed by a polynomial map of the interval B, C], where B 0 and C 1. We define the physically meaningful range for the parameters of the map, and we show that, within such a range, the map has a unique fixed point, which is stable and a global attractor, with the exception of one particular case, where bifurcation is observed. |
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Keywords: | Boltzmann chemical kinetics stability chaos entropy |
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