A 3D Strange Attractor with a Distinctive Silhouette. The Butterfly Effect Revisited

TL;DR

This paper introduces a novel 3D chaotic system with a unique strange attractor and demonstrates its sensitive dependence on initial conditions, including overlapping attractors, revisiting the Butterfly Effect.

Contribution

The paper presents a new autonomous 3D differential system with distinctive chaotic behavior and a novel attractor shape, expanding understanding of chaotic dynamics.

Findings

New 3D chaotic system with a unique attractor

Demonstrates sensitive dependence on initial conditions

Reveals overlapping attractors phenomenon

Abstract

We propose firstly an autonomous system of three first order differential equations which has two nonlinear terms and generating a new and distinctive strange attractor. Furthermore, this new 3D chaotic system performs a new feature of the Sensitive Dependency on Initial Conditions (SDIC) popularized as the Butterfly Effect discovered by Lorenz (1963). We noticed that the variation of the Initial Conditions for our system leads not only to different attractors but also to a singular phenomenon of overlapped attractors.