A Study Of Weak Attractor And Stability Theory Of Dynamical Systems

The topic of this paper is to concentrate on what is an attractor and show consider an exceptional class of this type of system and what is weak attractor and pullback , forward attractor and explain the difference between them and which one leads to the other through their definitions and do they have the same properties as the weak attractor. We concluded from this that every pullback attractor and forward attractor is weak attractor .Then we explain the stability theory of a dynamical system. We give characterizations of the stability theory in dynamical systems, We also study the Lyapunov stability and define this important theory, which is considered one of the most important theories , where it is ,Adynamical system is Lyapunov stable about an equilibrium point if state trajectories are confined to abounded region whenever the initial condition is chosen sufficiently close to equilibrium point .