Endotactic and strongly endotactic networks with infinitely many positive steady states

Abstract

We show that there exists endotactic and strongly endotactic dynamical systems that are not weakly reversible and possess infinitely many steady states. We provide a few examples in two dimensions and an example in three dimensions that satisfy this property. In addition, we prove for some of these systems that there exist no weakly reversible mass-action systems that are dynamically equivalent to mass-action systems generated by these networks.