  We consider the stability of nonlinear traveling waves in a class of
activator-inhibitor systems. The eigenvalue equation arising from linearizing
about the wave is seen to preserve the manifold of Lagrangian planes for a
nonstandard symplectic form. This allows us to define a Maslov index for the
wave corresponding to the spatial evolution of the unstable bundle. We
formulate the Evans function for the eigenvalue problem and show that the
parity of the Maslov index determines the sign of the derivative of the Evans
function at the origin. The connection between the Evans function and the
Maslov index is established by a "detection form," which identifies conjugate
points for the curve of Lagrangian planes.
