A mathematical model of an Agricultural-Industrial-Ecospheric system with industrial competition

In this paper we formulate a mathematical model using the predator-prey paradigm for study and analysis of the relationships between a complex four-dimensional system consisting of agriculture, two industries and the ecosphere. Mathematical analysis of the model equations with regard to invariance of nonnegativity, dissipativity (i.e. eventually boundedness) of solutions, and a complete local and global analysis of the system’s equilibria are done. We establish the existence of a positive interior equilibrium and give conditions under which such a system exhibits uniform persistence. The analysis is carried out both analytically and numerically.