  The Almost Hermitian Curvature flow was introduced by Streets and Tian in
order to study almost hermitian structures, with a particular interest in
symplectic structures. This flow is given by a diffusion-reaction equation.
Hence it is natural to ask the following: which almost hermitian structures are
dynamically stable? An almost hermitian structure $(\omega,J)$ is dynamically
stable if it is a fixed point of the flow and there exists a neighborhood
$\mathcal{N}$ of $(\omega,J)$ such that for any almost hermitian structure
$(\omega(0),J(0)) \in \mathcal{N}$ the solution of the Almost Hermitian
Curvature flow starting at $(\omega(0),J(0))$ exists for all time and converges
to a fixed point of the flow. We prove that on a closed K\"{a}hler-Einstein
manifold $(M,\omega,J)$ such that either $c_1(J) <0$ or $(M,\omega,J)$ is a
Calabi-Yau manifold, then the K\"{a}hler-Einstein structure $(\omega,J)$ is
dynamically stable.
