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September  2009, 8(5): 1689-1707. doi: 10.3934/cpaa.2009.8.1689

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

1. 

Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada

Received  January 2008 Revised  February 2009 Published  April 2009

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.
Citation: Ibrahim Agyemang, H. I. Freedman. A mathematical model of an Agricultural-Industrial-Ecospheric system with industrial competition. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1689-1707. doi: 10.3934/cpaa.2009.8.1689
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