  We prove dynamical stability and instability theorems for
Poincar\'{e}-Einstein metrics under the Ricci flow. Our key tool is a variant
of the expander entropy for asymptotically hyperbolic manifolds, which Dahl,
McCormick and the first author established in a recent article. It allows us to
characterize stability and instability in terms of a local positive mass
theorem and in terms of volume comparison for nearby metrics.
