  Diversity in the properties of exoplanetary systems arises, in part, from
dynamical evolution that occurs after planet formation. We use numerical
integrations to explore the relative role of secular and resonant dynamics in
the long-term evolution of model planetary systems, made up of three equal mass
giant planets on initially eccentric orbits. The range of separations studied
is dominated by secular processes, but intersects chains of high-order
mean-motion resonances. Over time-scales of $10^8$ orbits, the secular
evolution of the simulated systems is predominantly regular. High-order
resonant chains, however, can be a significant source of angular momentum
deficit (AMD), leading to instability. Using a time-series analysis based on a
Hilbert transform, we associate instability with broad islands of chaotic
evolution. Previous work has suggested that first-order resonances could modify
the AMD of nominally secular systems and facilitate secular chaos. We find that
higher-order resonances, when present in chains, can have similar impacts.
