Abstract
In this paper we constructed a Mathematical Model of food management for animal species interacting with natural environment. The mathematical framework has been generated with generations as the time scale. Efforts have been made to mathematically formalize the environmental changes dependent food availability and consequent changes. The aim to develop a mathematical perspective to understand the environmental impact on wild life population and its food management. The carrying capacity of environment in terms of primary food has been assumed to be limited. The environmental changes lead to changes in availability of vegetation for animal species. A Mathematical model is constructed in terms of a system of nonlinear difference equations. The solutions have been worked out for some special cases. These solutions can be expressed as finite polynomials. Graphical patterns have been worked out as examples
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