Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry

Research output: Contribution to journalJournal articleResearchpeer-review

  • Stefan Müller
  • Feliu, Elisenda
  • Georg Regensburger
  • Carsten Conradi
  • Anne Shiu
  • Alicia Dickenstein
We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomials maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determinants. In the context of chemical reaction networks with power-law kinetics, our results can be used to preclude as well as to guarantee multiple positive steady states. In the context of real algebraic geometry, our results reveal the first ...
Original languageEnglish
JournalFoundations of Computational Mathematics
Issue number1
Pages (from-to)69-97
Number of pages29
Publication statusPublished - 1 Feb 2016

ID: 94752755