A Mathematical Model of An Ecological System

Publication Year



mathematics, ecology, energy, cycling of nutrients, population


Applied Mathematics | Ecology and Evolutionary Biology | Mathematics | Physical Sciences and Mathematics


The purpose of this paper is to present a model that uses mathematics to describe a portion of an ecological system. The part of the ecosystem that is modeled here involves the processes of unidirectional transfer of energy and the cycling of nutrients.

The model is comprised of eight equations that describe the state of eight arbitrary populations within four energy levels over a period of time. There equations are formed by terms representing the above processes.

These terms are kept simple in nature so that the model can fit within the confines of a computer program already written to solve simultaneous non-linear differential equations. This program requires the conversion of the equations into a block oriented language.

The method used to test the model on the computer was to make one population operational before another was added. The simultaneous run of three populations always resulted in an overdamped solution.

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