Abdi Tadesse (PhD)Balcha Solomon2018-07-182023-11-042018-07-182023-11-042012-02http://etd.aau.edu.et/handle/123456789/9130The purpose of this study was to investigate the overall qualitative behavior of two dimensional linear systems such as classification of the systems from the dynamical point of view and in particular. To obtain insight in the classification of fixed point using trace and determinant of the coefficient matrix of planar systems; To develop classification criteria using trace and determinant of the coefficient matrix of the system, and also the way how to draw the trace determinant plane is discussed. To discuss the more subtle issue of topological equivalence (conjugacy) of these systems. Starting from simple planar linear systems and then we develop insight in investigating the relationship between two system that are topological conjugate and equivalent. Moreover, there is very important theorem mentioned in this project, the Hartman-Grobman theorem, which results in the local behavior theory of differential equations. The theorem shows near the hyperbolic fixed point, the non-linear system has the same qualitative structure as its linearizationenHartman-Grobman Theorem and Planar SystemsThesis