Structural stability on bifurcation theory

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.