Piecewise closed form expression of R\"ossler-like trajectories

TL;DR

This paper presents a method to analytically express R"ossler-like trajectories using piecewise functions, avoiding infinite series, and suggests potential extension to other attractors from experimental data.

Contribution

It introduces a novel piecewise closed-form approach for R"ossler-like trajectories that can be extended to other attractors without known differential equations.

Findings

Analytic expression of R"ossler-like trajectories achieved

Method avoids infinite series solutions

Potential applicability to other attractors from data

Abstract

The use of iteration and piecewise functions allows analytic expression of the trajectories of an R\"ossler-like attractor, avoiding infinite series solution. It seems possible to extend this approach to other attractors, even if the differential equations are not known, but the experimental data have been collected.