In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies within the very broad and natural class of weakly monotonic kinetics . In particular, multiple equilibria are precluded, as are degenerate positive equilibria. Moreover, under certain circumstances, also related to concordance, all real eigenvalues associated with a positive equilibrium are negative. Although concordance of a reaction network can be decided by readily available computational means, we show here that, when a nondegenerate network's Species Reaction Graph satisfies certain mild conditions, concordance and its dynamical consequences are ensured. These conditions are weaker than earlier ones invoked to establish kinetic system injectivity, which, in turn, is just one ramication of network concordance. Because the Species Reaction Graph resembles pathway depictions often drawn by biochemists, results here expand the possibility of inferring significant dynamical information directly from standard biochemical reaction diagrams.
In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies within the very broad and natural weakly monotonic class . In particular, multiple equilibria are precluded, as are degenerate positive equilibria. Moreover, under certain circumstances, also related to concordance, all real eigenvalues associated with a positive equilibrium are negative. Although concordance of a reaction network can be decided by readily available computational means, we show here that, when a nondegenerate network's Species-Reaction Graph satisfies certain mild conditions, concordance and its dynamical consequences are ensured. These conditions are weaker than earlier ones invoked to establish kinetic system injectivity, which, in turn, is just one ramification of network concordance. Because the Species-Reaction Graph resembles pathway depictions often drawn by biochemists, results here expand the possibility of inferring signicant dynamical information directly from standard biochemical reaction diagrams.
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class of weakly monotonic kinetics
weakly monotonic class
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Species Reaction
Species-Reaction
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ramication
ramification
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Species Reaction
Species-Reaction
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significant
signicant