A bifurcational geometric approach to the problem of chaos transition in the classical Lorenz system

TL;DR

This paper introduces a new bifurcational geometric approach to better understand the chaos transition in the classical Lorenz system, providing a novel scenario of how chaos emerges.

Contribution

It presents a new bifurcational geometric method to analyze the chaos transition in the Lorenz system, offering fresh insights into its attractor structure.

Findings

Proposes a new scenario of chaos transition

Utilizes bifurcational geometric approach

Provides numerical support for the scenario

Abstract

The classical Lorenz system is considered. For many years, this system has been the subject of study by numerous authors. However, until now the structure of the Lorenz attractor is not clear completely yet, and the most important question at present is to understand the bifurcation scenario of chaos transition in this system. Using some numerical results and our bifurcational geometric approach, we present a new scenario of chaos transition in the classical Lorenz system.