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2016

Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebrai

3 years 17 days ago
Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebrai
We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial 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 work recognizes a prior result of Craciun, Garcia-Puente, and Sottile, together with work of two of the authors, as the first partial multivariate generalization of the classical Descartes’ rule, which bounds the number of positive real roots of a univariate real polynomial in terms of the number of sign variations of its coefficients.
Stefan Müller 0009, Elisenda Feliu, Georg Reg
Added 03 Apr 2016
Updated 03 Apr 2016
Type Journal
Year 2016
Where FOCM
Authors Stefan Müller 0009, Elisenda Feliu, Georg Regensburger, Carsten Conradi, Anne Shiu, Alicia Dickenstein
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