Hayam Mohammed ElBarbary2018-08-012018-08-012008http://hdl.handle.net/123456789/12327A Thesis Submiiled in u fulfillment for Ph.'D degree in MathematicsAbstract The concept of dynamical system is discussed specially those containing critical points, fixed periodic points , the orbits of periodic points which lead to study the behavior of the system and it stability. We concentrate our discussion on Liapunov function and the bifurcations of equilibrium points; some application are discussed to clear the hole objective theory.enNonlinear SystemsThesis