  The Maslov index is a powerful tool for assessing the stability of solitary
waves. Although it is difficult to calculate in general, a framework for doing
so was recently established for singularly perturbed systems. In this paper, we
apply this framework to standing wave solutions of a three-component
activator-inhibitor model. These standing waves are known to become unstable as
parameters vary. Our goal is to see how this established stability criterion
manifests itself in the Maslov index calculation. In so doing, we obtain new
insight into the mechanism for instability. We further suggest how this
mechanism might be used to reveal new instabilities in singularly perturbed
models.
