Endotactic and strongly endotactic networks with infinitely many positive steady states

The dynamics exhibited by reaction networks is often a manifestation of their steady states. We show 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, 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. This extends a result by Boros, Craciun and Yu [1], who proved the existence of weakly reversible dynamical systems with infinitely many steady states.