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Multistationarity in Structured Reaction Networks. (arXiv:1810.05574v1 [q-bio.MN])
来源于:arXiv
Many dynamical systems arising in biology and other areas exhibit
multistationarity (two or more positive steady states with the same conserved
quantities). Although deciding multistationarity for a polynomial dynamical
system is an effective question in real algebraic geometry, it is in general
difficult to determine whether a given network can give rise to a
multistationary system, and if so, to identify witnesses to multistationarity,
that is, specific parameter values for which the system exhibits multiple
steady states. Here we investigate both problems. First, we build on work of
Conradi, Feliu, Mincheva, and Wiuf, who showed that for certain reaction
networks whose steady states admit a positive parametrization,
multistationarity is characterized by whether a certain "critical function"
changes sign. Here, we allow for more general parametrizations, which make it
much easier to determine the existence of a sign change. This is particularly
simple when the steady-state equations 查看全文>>