Homoclinic chaos in the R\"ossler model

TL;DR

This paper investigates the origins of homoclinic chaos in the Rössler model, analyzing bifurcations and attractor transformations using computational methods to understand chaotic dynamics.

Contribution

It introduces tailored computational techniques to analyze homoclinic bifurcations and stability regions in the Rössler model's parameter space.

Findings

Identification of bifurcation structures leading to chaos

Mapping of stable and chaotic regions in parameter space

Insights into the global unfolding of the Rössler attractors

Abstract

We study the origin of homoclinic chaos in the classical 3D model proposed by O. R\"ossler in 1976. Of our particular interest are the convoluted bifurcations of the Shilnikov saddle-foci and how their synergy determines the global unfolding of the model, along with transformations of its chaotic attractors. We apply two computational methods proposed, 1D return maps and a symbolic approach specifically tailored to this model, to scrutinize homoclinic bifurcations, as well as to detect the regions of structurally stable and chaotic dynamics in the parameter space of the R\"ossler model.