In this thesis we deal with mathematical models that illustrate the growth of two populations, which influence each other and between them appears one of the three main potential interactions between two populations: competition for resources, predation or symbiosis. We begin by examining the two-dimensional linear systems of differential equations – more precisely examining the way of finding solutions of two-dimensional linear homogeneous systems of two differential equations. Then we dedicate to two-dimensional nonlinear autonomous system and its linearization around fixed points. This allows us to study three mathematical models of different interactions between two populations, which also conclude the study.
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