Nonlinear systems and stability analysis

Nonlinear dynamic systems are very important subject of scientific researchers recently. Real natural phenomena have nonlinear characters so that in basic science, engineering social and economy sciences the most of model studies have nonlinear dynamic behavior. In this thesis some physical and engineering examples of nonlinear systems and related mathematical nonlinear equations are I given. Time evolution of nonlinear dynamical systems are not easy to study analytically, so that the methods to study these systems are introduced. Phase space of the nonlinear systems are introduced and some specific definitions such as trajectories and critical points are defined. By using phase space analysis and some related theorems the stability of the nonlinear systems are discussed. The general procedure given in thesis are applied to nonlinear conservative systems. Keywords: Nonlinear systems, stability, critical points, phase space.