In my diploma thesis I deal with autonomous dynamical systems in a plane given by a system of two differential equations. The central goal of the diploma is the proof and application of the Poincare-Bendixson theorem. The mentioned theorem defines the possible limit behaviors of bounded trajectories, so it is very useful in predicting the behavior of these systems at large times. In the paper, we will apply the theorem to the economic model, which includes structural changes. These occur due to various factors in the economy, such as changes in economic development or lack of resources. We will show how all of these factors can be illustrated by a dynamic system whose behavior is predictable according to Poincare-Bendixson's theorem. More precisely, we will implement and discuss the Kaldor model, and expand it to the field of Slovenian healthcare.
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