Geometry Seminar

Date: October 27, 2017

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Xiaoxian Tang, TAMU

Title: Investigating multistationarity in structured reaction networks

Abstract: Many dynamical systems arising in applications exhibit multistationarity (two or more positive steady states), but it is often difficult to determine whether a given system is multistationary, and if so to identify a witness to multistationarity, that is, specific parameter values for which the system exhibits multiple steady states. Here we investigate both problems. We prove two new sufficient conditions for multistationarity: (1) when there are no boundary steady states and a certain critical function changes sign, and (2) when the steady-state equations can be replaced by equivalent triangular-form equations. We also investigate the mathematical structure of this critical function, and give conditions that guarantee that triangular-form equations exist.