Finding invariant sets for biological systems using monomial domination

In this paper we present a novel approach to the analysis of nonnegative dynamical systems whose vector fields are polynomial or rational functions. Our analysis framework is based on results developed and presented in a previous study on general conditions that imply non-vanishing of polynomial functions on the positive orthant. This approach is due to the sparsity of the negative terms in the polynomial, which are then “dominated” by the positive terms. Particularly, we present a novel approach to find invariant sets of a dynamical system and one to aid the search for the number of possible equilibria of the system. To illustrate this approach we apply it to a model of a food web to check for overpopulation or extinction of species.