Unraveling the Chaos-land and its organization in the Rabinovich System

TL;DR

This paper employs advanced symbolic and computational techniques to analyze the intricate global organization of chaos in the Rabinovich system, revealing complex bifurcation structures and organizing centers.

Contribution

It develops a comprehensive suite of analytical tools, including DCP, to uncover the detailed bifurcation and chaos structures in the Rabinovich system.

Findings

Identification of homoclinic and heteroclinic connections

Revelation of codimension-2 Bykov T-points

Mapping of simple and chaotic dynamics regions

Abstract

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.