Coexistence of periods in a bisecting bifurcation

TL;DR

This paper investigates the complex structure of attractors in a population model, revealing the coexistence of multiple neutrally stable limit cycles with different periods during bifurcation to chaos.

Contribution

It provides an algebraic and geometric explanation for the coexistence of a continuum of neutrally stable limit cycles in the bifurcation from regular to chaotic behavior.

Findings

Coexistence of a continuum of neutrally stable limit cycles identified

Algebraic and geometric methods used to explain attractor structure

Insights into bifurcation from regular to chaotic dynamics

Abstract

The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.