  A suite of analytical and computational techniques based on symbolic
representations of simple and complex dynamics, is further developed and
employed to unravel the global organization of bi-parametric structures that
underlie the emergence of chaos in a simplified resonantly coupled wave triplet
system, known as the Rabinovich system. Bi-parametric scans reveal the stunning
intricacy and intramural connections between homoclinic and heteroclinic
connections, and codimension-2 Bykov T-points and saddle structures, which are
the prime organizing centers of complexity of the bifurcation unfolding of the
given system. This suite includes Deterministic Chaos Prospector (DCP) to sweep
and effectively identify regions of simple (Morse-Smale) and chaotic
structurally unstable dynamics in the system. Our analysis provides striking
new insights into the complex behaviors exhibited by this and similar systems.
