An environmental model for the interactions of industry with two competing agricultural resources

Authors:
Ibrahim Agyemang;H. I. Freedman
Affiliations:
Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada;Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

Citing 6
Cited 0

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Abstract

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.