Cyklisk jakt och flykt i planet

Sammanfattning: Let n bugs constitute the corners of an n-sided polygon. If the bugs cyclically pursue each other, the positions of the bugs will satisfy a system of ordinary differential equations, which we study. We examine the system for different n, but focus on the case n=3. When n=3, the bugs form a triangle. In this case, the solution will converge to some point. We study how the convergence occur. Ignoring translation, rotation and scaling, the triangle converges to a line. Further, we also consider when the three bugs escape from each other. If we again ignore rotation, translation and scaling, the triangle converges to an equilateral triangle. Finally, most theory in this thesis is already known, but we present a new proof for the convergence when three bugs pursuit each other.