Foundations of Chemical Reaction Network Theory pp 419-440 | Cite as

# Species-Reaction Graph Foundations

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## Abstract

The very powerful Theorem 11.6.1 told us that, when a nondegenerate network’s Species-Reaction Graph satisfies certain mild conditions, behavior is severely constrained to be largely stable and dull, provided only that the kinetics associated with the network resides in the large and natural weakly monotonic class. The underlying idea was that, when those graphical conditions are satisfied, the network’s fully open extension is concordant. Nondegeneracy of the original network then ensured that it too is concordant, in which case the original network inherits all the dynamical attributes that concordance mandates.

## References

- 21.Biggs, N.: Algebraic Graph Theory. Cambridge University Press (1994)Google Scholar
- 24.Bondy, A., Murty, U.: Graph Theory. Springer, New York (2010)zbMATHGoogle Scholar
- 62.Ellison, P., Ji, H., Knight, D., Feinberg, M.: The Chemical Reaction Network Toolbox, Version 2.3 (2014). Available at https://crnt.osu.edu
- 87.Gale, D.: The Theory of Linear Economic Models. University of Chicago Press, Chicago (1960)zbMATHGoogle Scholar
- 117.Knight, D.: Reactor behavior and its relation to chemical reaction network structure. Ph.D. thesis, The Ohio State University (2015)Google Scholar
- 118.Knight, D., Shinar, G., Feinberg, M.: Sharper graph-theoretical conditions for the stabilization of complex reaction networks. Mathematical Biosciences
**262**(1), 10–27 (2015)MathSciNetCrossRefGoogle Scholar - 158.Shinar, G., Feinberg, M.: Concordant chemical reaction networks and the species-reaction graph. Mathematical Biosciences
**241**(1), 1–23 (2013)MathSciNetCrossRefGoogle Scholar - 176.Wilson, R.J.: Introduction to Graph Theory. Addison-Wesley, Reading, MA (1996)zbMATHGoogle Scholar

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