  In this paper, we develop and analyze a model that studies the interaction
between a specialist predator, a generalist predator, and their common prey in
a two-trophic ecosystem featuring three timescales. We assume that the prey
operates on a faster timescale, while the specialist and generalist predators
operate on slow and superslow timescales respectively. Treating the predation
efficiency of the generalist predator as the primary varying parameter and the
proportion of its diet formed by the prey species under study as the secondary
parameter, we obtain a host of rich and interesting dynamics, including
relaxation oscillations, mixed-mode oscillations (MMOs), subcritical elliptic
bursting patterns, torus canards, and mixed-type torus canards. By grouping the
timescales into two classes and using the timescale separation between classes,
we apply one-fast/two-slow and two-fast/one-slow analysis techniques to gain
insights about the dynamics. Using the geometric properties and flows of the
singular subsystems, in combination with bifurcation analysis and numerical
continuation of the full system, we classify the oscillatory dynamics and
discuss the transitions from one type of dynamics to the other. The types of
oscillatory patterns observed in this model are novel in population models
featuring three-timescales; some of which qualitatively resemble natural cycles
in small mammals and insects. Furthermore, oscillatory dynamics displaying
torus canards, mixed-type torus canards, and MMOs experiencing a delayed loss
of stability near one of the invariant sheets of the self-intersecting critical
manifold before getting attracted to the adjacent attracting sheet of the
critical manifold have not been previously reported in three-timescale models.
