Homoclinic puzzles and chaos in a nonlinear laser model

TL;DR

This paper investigates complex bifurcation structures and chaos in a nonlinear laser model, combining traditional continuation methods with a novel GPU-accelerated symbolic dynamics technique to reveal detailed bifurcation patterns.

Contribution

It introduces the Deterministic Chaos Prospector (DCP), a new GPU-based method for analyzing bifurcations and chaos in nonlinear dynamical systems, complementing existing tools.

Findings

Identification of homoclinic and heteroclinic bifurcation structures

Visualization of bifurcation surfaces and chaos regions in parameter space

Detailed reconstruction of key bifurcation phenomena like Bykov T-points

Abstract

We present a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the 2D and 3D parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor. In a symbiotic approach combining the traditional parameter continuation methods using MatCont and a newly developed technique called the Deterministic Chaos Prospector (DCP) utilizing symbolic dynamics on fast parallel computing hardware with graphics processing units (GPUs), we exhibit how specific codimension-two bifurcations originate and pattern regions of chaotic and simple dynamics in this classical model. We show detailed computational reconstructions of key bifurcation structures such as Bykov T-point spirals and inclination flips in 2D parameter space, as well as the spatial organization and 3D embedding of bifurcation surfaces, parametric saddles, and isolated closed curves (isolas).