Abstract:
In this research we classify the continuily and discrete time linear systems .we Also discuss the equilibrium point for some standard systems by using the Flow-box theorem and Hartman-Grobman theorems with some
applications in term of center manifolds.
We also discuss some new methods for studying the global phase portrait in general , and then introduce the index theory of the vectors fields in two dimensions with some examples . We illustrate the Bifurcation theory and we study some standard Bifurcations. We also discuss the structural stability of one–dimension system with some applications and examples.
