  Microresonators are micron-scale optical systems that confine light using
total internal reflection. These optical systems have gained interest in the
last two decades due to their compact sizes, unprecedented measurement
capabilities, and widespread applications. The increasingly high finesse (or
$Q$ factor) of such resonators means that nonlinear effects are unavoidable
even for low power, making them attractive for nonlinear applications,
including optical comb generation and second harmonic generation. In addition,
light in these nonlinear resonators may exhibit chaotic behavior across wide
parameter regions. Hence, it is necessary to understand how, where, and what
types of such chaotic dynamics occur before they can be used in practical
devices. We consider a pair of coupled differential equations that describes
the interactions of two optical beams in a single-mode resonator with symmetric
pumping. Recently, it was shown that this system exhibits a wide range of
fascinating behaviors, including bistability, symmetry breaking, chaos, and
self-switching oscillations. We employ here a dynamical system approach to
identify, delimit, and explain the regions where such different behaviors can
be observed. Specifically, we find that different kinds of self-switching
oscillations are created via the collision of a pair of asymmetric periodic
orbits or chaotic attractors at Shilnikov homoclinic bifurcations, which acts
as a gluing bifurcation. We present a bifurcation diagram that shows how these
global bifurcations are organized by a Belyakov transition point (where the
stability of the homoclinic orbit changes). In this way, we map out distinct
transitions to different chaotic switching behavior that should be expected
from this optical device.
