Ecological chains and their mathematical and computer models

Abstract

The article deals with the problem of studying the structures and evolutions of ecological chains at the level of microorganisms using mathematical and computer models. Several mathematical models have been constructed based on the laws of biological kinetics. Computer experiments were developed using these models. Mathematical models describing the dependence of the concentration of bacterial biomass, substrates and protozoa on time have been created. With the help of the Mathcad package, graphical solutions of mathematical models were obtained and analyzed. 

Graphs of the states of ecological chains with changes in the rate of penetration of the nutrient substrate into the system were created and these states were studied. Mathematical models describing the mutual competition of 6 different bacteria were developed in Mathcad environment. The parameters characterizing the biomass concentration of each bacterium were established. This parameter included: saturation constant of bacteria, saturation constant of protozoa, maximum value of specific growth rate of bacteria, maximum value of specific growth rate of protozoa, and economic growth coefficient of protozoa. Graphical solution of mathematical models have been analyzed. These models characterize the dynamics of the concentration of bacterial biomass.

A computer experiment representing competition between bacterial species was developed. The results of mutual competition of ten different bacterial colonies were obtained on the basis of numerical and graphical methods. The software has been compiled in Microsoft Visual Basic 6.0 environment.