Abstract:
In this research we consider the most useful
methods to study the flow near bifurcation point,
that is the center manifolds theorem. Because of
this way study the Dynamical Systems and there
geometrical theory with some examples. Also we
discuss the basic concepts of studying dynamical
system with some applications. We discuss the
stationary and periodic solutions and we illustrate
how to determine relations between linear or
nonlinear stability. Also we study the center
manifolds and their prosperities. We discuss the
bifurcations involving a single or several eigenvalues
with some applications and examples.
