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Mixed volume of
small reaction networks
Nida Obatake, Anne Shiu and Dilruba Sofia
Vol. 13 (2020), No. 5, 845–860
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Abstract |
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An important invariant of a chemical reaction network is its maximum number of positive steady states. This number, however, is in general difficult to compute. Nonetheless, there is an upper bound on this number — namely, a network’s mixed volume — that is easy to compute. Moreover, recent work has shown that, for certain biological signaling networks, the mixed volume does not greatly exceed the maximum number of positive steady states. Continuing this line of research, we further investigate this overcount and also compute the mixed volumes of small networks, those with only a few species or reactions. |
Keywords
chemical reaction network, steady state, Newton polytope,
mixed volume
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Mathematical Subject Classification
Primary: 52A39, 12D10, 37C10
Secondary: 65H04, 80A30
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Milestones
Received: 1 May 2020
Revised: 10 September 2020
Accepted: 20 September 2020
Published: 5 December 2020
Communicated by Suzanne Lenhart
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Authors |
| Nida Obatake | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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| Anne Shiu | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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| Dilruba Sofia | |
| Department of Mathematics and
Statistics University of Massachusetts Amherst, MA United States |
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