Samay Kothari supervised by Dr. Abhishek Deshpande received his  Master of Science –  Dual Degree in Computational Natural Sciences  (CND). Here’s a summary of his research work on Endotactic and strongly endotactic networks with infinitely many positive steady states and Realizations through Weakly Reversible Networks and the Globally Attracting Locus:

The dynamics exhibited by reaction networks is often a manifestation of their steady states. This dissertation shows that there exists endotactic and strongly endotactic dynamical systems that are not weakly reversible and possess a family of infinitely many positive steady states. In addition, for some of these systems we prove that there exist no weakly reversible mass-action systems that are dynamically equivalent to mass-action systems generated by these networks. This extends a result by Boros, Craciun and Yu [1], who proved the existence of weakly reversible dynamical systems with infinitely many steady states. We also investigate the possibility that for any given reaction rate vector k associated with a network G, there exists another network G′ with a corresponding reaction rate vector that reproduces the mass action dynamics generated by (G,k). Our focus is on a particular class of networks for G, where the corresponding network G′ is weakly reversible. In particular, we show that strongly endotactic two dimensional networks with a two-dimensional stoichiometric subspace, as well as certain endotactic networks under additional conditions, exhibit this property. Furthermore, we show that being endotactic is necessary for the dynamics of a network to be included in the dynamics of a weakly reversible network. Additionally, we establish a strong connection between this family of networks and the locus in the space of rate constants in which the corresponding dynamics admits globally stable steady states.

August 2025