Abstract: Toric dynamical systems are polynomial dynamical systems that appear naturally as models of reaction networks and have very robust and stable properties. A disguised toric dynamical system is a polynomial dynamical system generated by a reaction network and some choice of positive parameters, such that it has a toric realization with respect to some other network. Disguised toric dynamical systems enjoy all the robust stability properties of toric dynamical systems. In this project, we study a larger set of dynamical systems where the rate constants are allowed to take both positive and negative values. More precisely, we analyze the R-disguised toric locus of a reaction network, i.e., the subset in the space rate constants (positive or negative) for which the corresponding polynomial dynamical system is disguised as toric In particular, we construct homeomorphisms to provide an exact bound on the dimension of the
R-disguised toric locus. This is a joint work with Gheorghe Craciun and Abhishek Deshpande.

Joint work with  Gheorghe Craciun (WISC), Abhishek Deshpande (IIIT Hyderabad).

Zoom link is available from the organizer of the seminar. Please contact János Tóth at jtoth(at)math.bme.hu. 

Paper: https://link.springer.com/article/10.1007/s10910-023-01533-0