Limit models in strictly stable abstract elementary classes

In this paper, we examine the locality condition for non-splitting and determine the level of uniqueness of limit models that can be recovered in some stable, but not superstable, abstract elementary classes. In particular we prove the following. Suppose that $K$ is an abstract elementary class satisfying

Then for $\vartheta$ and $\delta$ limit ordinals both with cofinality $\ge {\kappa }_{\mu }^{\ast }\left(K\right)$, if $K$ satisfies symmetry for $\mathrm{non}-\mu -\mathrm{splitting}$ (or just $(\mu ,\delta )$-symmetry), then, for any $M_1$ and $M_2$ that are $(\mu ,\vartheta )$ and $(\mu ,\delta )$-limit models over $M_0$, respectively, we have that $M_1$ and $M_2$ are isomorphic over $M_0$. Note that no tameness is assumed.