Multifractal analysis of intermingled basins and blowout bifurcations in a parametetric family of skew product maps

2025/02/07 by Ghane, Fatemeh Helen, Kesseböhmer, Marc
#37C40 #37C45 #37C70 #37H15 #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.2502.04869

Abstract

In this paper we study a two-parameter family of planar maps characterized by two distinct invariant subspaces. The model reveals the existence of two chaotic attractors within these subspaces. We identify parameter values at which these attractors either exhibits a locally riddled basin of attraction or transitions into a chaotic saddle. In particular, we demonstrate that, for an open region in the parameter plane, their basins are intermingled. It is shown that a fractal boundary curve separates the basins of attraction of these two chaotic attractors, providing a detailed characterization of the riddled basin structure. Additionally, we show that the model undergoes a blowout bifurcation. An estimation of the stability index is examined using thermodynamic formalism. We also perform a multifractal analysis of the level sets of the stability index.

Related

• The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps
• Border-collision bifurcations from stable fixed points to any number of coexisting chaotic attractors
• Fractal Basins and Boundaries in 2D Maps inspired in Discrete Population Models
• Fractalization of Torus Revisited as a Strange Nonchaotic Attractor
• Bernoulli mapping with hole and a saddle-node scenario of the birth of hyperbolic Smale--Williams attractor