Flow curvature manifolds for shaping chaotic attractors: Rossler-like systems

TL;DR

This paper investigates how flow curvature manifolds influence the structure of Rossler-like chaotic attractors, revealing their role in shaping attractors and explaining limitations in chaotic regime development.

Contribution

It introduces the use of flow curvature manifolds to analyze the structure of chaotic attractors, extending understanding beyond fixed points.

Findings

Flow curvature manifolds structure Rossler-like attractors

These manifolds explain limitations in chaotic regime development

Time-dependent components are key to understanding attractor shape

Abstract

Poincar\'e recognized that phase portraits are mainly structured around fixed points. Nevertheless, the knowledge of fixed points and their properties is not sufficient to determine the whole structure of chaotic attractors. In order to understand how chaotic attractors are shaped by singular sets of the differential equations governing the dynamics, flow curvature manifolds are computed. We show that the time dependent components of such manifolds structure Rossler-like chaotic attractors and may explain some limitation in the development of chaotic regimes.