A Novel Strange Attractor with a Stretched Loop

TL;DR

This paper presents a new 3D strange attractor derived from a modified Lotka-Volterra system, exhibiting unique topological features and diverse oscillatory behaviors, expanding the understanding of chaotic dynamical systems.

Contribution

It introduces a novel strange attractor with a distinct topology and analyzes its global dynamics and oscillatory regimes.

Findings

The attractor can transition from double scroll to single scroll with a stretched loop.

The model exhibits a range of periodic and a-periodic oscillations.

The attractor's topology is unique among known chaotic systems.

Abstract

The paper introduces a new 3D strange attractor topologically different from any other known chaotic attractors. The intentionally constructed model of three autonomous first-order differential equations derives from the coupling-induced complexity of the well-known Lotka-Volterra oscillator. The chaotic attractor exhibiting a double scroll bridged by a loop mutates to a single scroll with a very stretched loop by the variation of one parameter. Analysis of the global behavior of the new low dimensional dissipative dynamical model and its range of periodic and a-periodic oscillations are presented.