An Environmental Model for the Interactions of Industry with Two Competing Agricultural Resources

In this paper we model the interactive dynamics between normal agriculture, auxiliary agriculture, industry and the ecosphere using a system of ordinary non-linear differential equations. We study the long-term effects of each of these assets on each other. Mathematical analyses of the model equations with regard to invariance of non-negativity, dissipativity of solutions, and local and global analyses of the system's equilibria are carried out. We establish conditions for the existence of a positive interior equilibrium using the theory of uniform persistence.