  In this paper we present some local dynamic bifurcation results in terms of
invariant sets of nonlinear evolution equations. We show that if the trivial
solution is an isolated invariant set of the system at the critical value
$\lambda=\lambda_0$, then either there exists a one-sided neighborhood $I^-$ of
$\lambda_0$ such that for each $\lambda\in I^-$, the system bifurcates from the
trivial solution to an isolated nonempty compact invariant set $K_\lambda$ with
$0\not\in K_\lambda$, or there is a one-sided neighborhood $I^+$ of $\lambda_0$
such that the system undergoes an attractor bifurcation for $\lambda\in I^+$
from $(0,\lambda_0)$. Then we give a modified version of the attractor
bifurcation theorem. Finally, we consider the classical Swift-Hohenberg
equation and illustrate how to apply our results to a concrete evolution
equation.
