Homoclinic chaos and its organization in a nonlinear optics model

TL;DR

This paper introduces a computational method that simplifies the analysis of chaos in nonlinear systems by reducing dynamics to symbolic representations, enabling rapid and detailed bifurcation analysis.

Contribution

It presents a novel, efficient computational approach that uses symbolic binary reduction and parallel simulations to study homoclinic chaos in nonlinear optics models.

Findings

Rapid bifurcation diagram generation within seconds

Identification of simple and complex dynamical regions

Enhanced understanding of chaos onset mechanisms

Abstract

We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the reduction of phase space dynamics to symbolic binary representations that lets one detect regions of simple and complex dynamics as well as fine organization structures of the latter in parameter space. Massively parallel simulations shorten the computational time to disclose highly detailed bifurcation diagrams to a few seconds.