Stability analysis of dynamical systems

STABILITY ANALYSIS OF DYNAMICAL SYSTEMS SUMMARY Keywords : Stability, Phase Plane, Autonomous System, Bifurcation and Chaos In this study, the qualitative analysis in a circumstance modelled with a differential equation is done. There are two important subjects in the differantial equation systems. First one is existence and uniqueness of solution. Second one is the stability or instability of the system. It is important that small changing in some parameters and initial data how affects solutions, what is the asymptotic behaviour of the solutions, are there periodical solutions in the system and does the system show chaotic behaviour? Examining these type behaviours is also possible by obtaining analytical solutions of the system. In this thesis, the subject characterized as qualitative analysis was taken elementary level, performed and given an example. Also analysis of some important dynamical systems were given.