  Two entropic dynamical models are considered. The geometric structure of the
statistical manifolds underlying these models is studied. It is found that in
both cases, the resulting metric manifolds are negatively curved. Moreover, the
geodesics on each manifold are described by hyperbolic trajectories. A detailed
analysis based on the Jacobi equation for geodesic spread is used to show that
the hyperbolicity of the manifolds leads to chaotic exponential instability. A
comparison between the two models leads to a relation among statistical
curvature, stability of geodesics and relative entropy-like quantities.
Finally, the Jacobi vector field intensity and the entropy-like quantity are
suggested as possible indicators of chaoticity in the ED models due to their
similarity to the conventional chaos indicators based on the Riemannian
geometric approach and the Zurek-Paz criterion of linear entropy growth,
respectively.
