Browsing by Author "Girmay Fasil"

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    On Poincar´e-Bendixson Theorem and Closed Orbits of Nonlinear Dynamical Systems
    (Addis Ababa University, 2012-02) Girmay Fasil; Abdi Tadesse (PhD)
    In a certain sense, closed orbits are the only types of orbits that we can ever hope to understand completely throughout their evolution from the distant past (i.e. as t ! −1) to the distant future (i.e., as t ! 1) since the entire course of their evolution is determined by knowledge over a finite time interval, i.e., the period. Like equilibrium points that are asymptotically stable, periodic solutions may also attract other solutions. Determining the long time behavior of closed orbits is much more difficult while in this project paper we do have a tool that resembles the linearization technique called the Poincar´e map. Furthermore, by applying the Poincar´e-Bendixson theorem the limiting behaviors of a planar flow is determined.