Development and Analysis of Some Mathematical Models in Population Biology
Date of Graduation
Master of Science in Mathematics
differential equations, population biology, mathematical models, population dynamics, growth models
Differential equations can be quite beneficial as mathematical models in the study of population dynamics. The purpose of this study is to observe some benefits differential equations bring to specific areas of research in the field of population biology including the control of fish populations through the regulation of fishing, observing a possible risk in the use of insecticides, and predicting the growth patterns of tumors in hopes of discovering potential treatments. In order to achieve this, we examine the development and analysis of some mathematical models of population biology on a more general spectrum. We begin by developing possible models for the population growth of a single species, then expand our research to the development of more complex models involving two or more species interacting with each other in different ways. Quantitative analysis of some of the more simplistic models is used in order to evaluate the dependability of the model for representing the growth of one or more populations. However, we primarily focus on qualitative analysis necessary in evaluating more complex models that cannot be solved explicitly. This qualitative analysis includes examining the behavior of the models near equilibrium points by interpretation of the graphs of the models, using linear approximations of the equations, as well as the use of theorems such as the Liapunov theorem.
© Angela D. Shreckhise
Shreckhise, Angela D., "Development and Analysis of Some Mathematical Models in Population Biology" (2004). MSU Graduate Theses. 1615.