Establishing multistationarity conditions for polynomial ODEs in biology

Date: 4/3/2019
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Abstract:Polynomial Ordinary Differential Equations are an important tool in many areas of quantitative biology. Due to large measurement uncertainty, few experimental repetitions and a limited number of measurable components, parameter values are accompanied by large confidence intervals. One therefore effectively has to study families of parametrized polynomial ODEs. Multistationarity, that is the existence of at least two positive solutions to the steady state equations has been recognized as an important qualitative property of these ODEs. As a consequence of parameter uncertainty numerical analysis often fails to establish multistationarity. Hence techniques allowing the analytic computation of parameter values where a given system exhibits multistationarity are desirable. In my talk I focus on ODEs that are dissipative and where additionally the steady state variety admits a monomial parameterization. For such systems multistationarity can be decided by studying the sign of the determinant of the Jacobian evaluated at this parameterization. I present examples where this allows to determine semi-algebraic descriptions of parameter regions for multistationarity.