Homoclinic chaos in the Rössler model.

We study the origin of homoclinic chaos in the classical 3D model proposed by Rössler in 1976. Of our particular interest are the convoluted bifurcations of the Shilnikov saddle-foci and how their synergy determines the global bifurcation unfolding of the model, along with transformations of its chaotic attractors. We apply two computational methods proposed, one based on interval 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 Rössler model.