Coexisting patterns of population oscillations: the degenerate Neimark Sacker bifurcation as a generic mechanism

TL;DR

This paper studies a population model showing how a Neimark Sacker bifurcation leads to coexisting oscillation patterns, including period locking and the emergence of a second attractor, highlighting natural bifurcation mechanisms.

Contribution

It demonstrates that coexisting oscillation patterns arise naturally from bifurcations in population models, with detailed analysis of period locking and attractor coexistence.

Findings

Period locking at period 4 occurs after bifurcation.

A second attractor with period 2 coexists over a parameter range.

Bifurcations producing the second attractor are natural in the system.

Abstract

We investigate a population dynamics model that exhibits a Neimark Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period becomes soon locked at 4 due to a strong resonance, and a second attractor of period 2 emerges, which coexists with the first attractor over a considerable parameter range. A linear stability analysis and a numerical investigation of the second attractor reveal that the bifurcations producing the second attractor occur naturally in this type of system.