Intraspecific dominance in competitive interactions

The purpose of this thesis is to investigate mathematical interpretations of intraspecific dominance in competitive interactions.

The Introduction and Chapter 1 provide some motivation for the thesis and define most of the terminology used in the text. In Chapter 2 conditions are defined that can be interpreted as intraspecific competitive dominance. These conditions are used to prove the existence of a unique positive equilibrium for the general Kolmogorov model with certain assumptions. In Chapter 3 one more condition is defined that can be interpreted as a condition of "balance" in the competitive community. The balance condition and the conditions of intraspecific competitive dominance are used to prove that a positive equilibrium is locally asymptotically stable.