Period doubling in the Rossler system - a computer assisted proof

TL;DR

This paper presents a computer-assisted method to rigorously produce bifurcation diagrams of periodic orbits in the Rossler system, demonstrating the occurrence of two period doubling bifurcations within a specific parameter range.

Contribution

It introduces a novel computer-assisted approach to rigorously verify bifurcation diagrams in nonlinear ODEs, specifically applied to the Rossler system.

Findings

Confirmed the existence of two period doubling bifurcations in the Rossler system.

Provided a rigorous bifurcation diagram for the studied parameter range.

Demonstrated the effectiveness of computer-assisted proofs in nonlinear dynamics.

Abstract

The goal of this paper is to show how to produce a piece of rigorous bifurcation diagram of periodic orbits for an ODE. We study the Rossler system, one of the textbook examples of ODEs generating nontrivial dynamics, for the parameter range containing two period doubling bifurcations.