Recent Issues
Volume 17, 4 issues
Volume 17
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182
Volume 16, 5 issues
Volume 16
Issue 5, 727–903
Issue 4, 547–726
Issue 3, 365–546
Issue 2, 183–364
Issue 1, 1–182
Volume 15, 5 issues
Volume 15
Issue 5, 727–906
Issue 4, 547–726
Issue 3, 367–546
Issue 2, 185–365
Issue 1, 1–184
Volume 14, 5 issues
Volume 14
Issue 5, 723–905
Issue 4, 541–721
Issue 3, 361–540
Issue 2, 181–360
Issue 1, 1–179
Volume 13, 5 issues
Volume 13
Issue 5, 721–900
Issue 4, 541–719
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180
Volume 12, 8 issues
Volume 12
Issue 8, 1261–1439
Issue 7, 1081–1260
Issue 6, 901–1080
Issue 5, 721–899
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180
Volume 11, 5 issues
Volume 11
Issue 5, 721–900
Issue 4, 541–720
Issue 3, 361–540
Issue 2, 181–359
Issue 1, 1–179
Volume 10, 5 issues
Volume 10
Issue 5, 721–900
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180
Volume 9, 5 issues
Volume 9
Issue 5, 721–899
Issue 4, 541–720
Issue 3, 361–540
Issue 2, 181–359
Issue 1, 1–180
Volume 8, 5 issues
Volume 8
Issue 5, 721–900
Issue 4, 541–719
Issue 3, 361–540
Issue 2, 181–359
Issue 1, 1–179
Volume 7, 6 issues
Volume 7
Issue 6, 713–822
Issue 5, 585–712
Issue 4, 431–583
Issue 3, 245–430
Issue 2, 125–244
Issue 1, 1–124
Volume 6, 4 issues
Volume 6
Issue 4, 383–510
Issue 3, 261–381
Issue 2, 127–260
Issue 1, 1–126
Volume 5, 4 issues
Volume 5
Issue 4, 379–504
Issue 3, 237–378
Issue 2, 115–236
Issue 1, 1–113
Volume 4, 4 issues
Volume 4
Issue 4, 307–416
Issue 3, 203–305
Issue 2, 103–202
Issue 1, 1–102
Volume 3, 4 issues
Volume 3
Issue 4, 349–474
Issue 3, 241–347
Issue 2, 129–240
Issue 1, 1–127
Volume 2, 5 issues
Volume 2
Issue 5, 495–628
Issue 4, 371–494
Issue 3, 249–370
Issue 2, 121–247
Issue 1, 1–120
Volume 1, 2 issues
Volume 1
Issue 2, 123–233
Issue 1, 1–121
Abstract
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
Mathematical Subject Classification
Primary: 52A39, 12D10, 37C10
Secondary: 65H04, 80A30
Milestones
Received: 1 May 2020
Revised: 10 September 2020
Accepted: 20 September 2020
Published: 5 December 2020
Communicated by Suzanne Lenhart