Systems of nonlinear equations deriving from complex chemical reaction networks

The capacity for multiple equilibria in an isothermal homogeneous continuous flow stirred tank reactor is determined by the reaction network. Examples show that there is a very delicate relationship between reaction network structure and the possibility of multiple equilibria. Previous results of Schlosser and Feinberg are sufficiently refined as to identify subtle differences between networks that can admit multiple equilibria and very sim­ ilar ones that cannot, based on a graph associated to the reaction network, called the SCL graph. The SCL graph method cannot be easily implemented as a computer algorithm, and does not give an answer for some reaction networks. We suggest two new methods of solving this problem. One method can be im­ plemented as a simple computer algorithm, and is more general than the SCL graph method. The other method is based on a new type of graph associated to the reaction network, called the SR graph, and gives an answer for many reaction networks for which the SCL graph method does not.

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