Math 6410 • ODE

\begin{enumerate}
\item[(a)] State the Center Manifold Theorem for rest points. Briefly explain its
importance in bifurcation theory.
\item[(b)] Using an approximate center manifold, determine the nature of the bifurcation
from \((x,\dot{x},\epsilon)=(0,0,0)\) for the quadratic Duffing's Equation
\[
  \ddot{x}+\dot{x}+\epsilon x+x^2=0.
\]
\end{enumerate}