Extinction, periodicity and multistability in a Ricker Model of Stage-Structured Populations

TL;DR

This paper analyzes a two-stage population model using a Ricker difference equation, identifying conditions for extinction and complex multistable dynamics, including periodic and non-periodic orbits.

Contribution

It provides new sufficient conditions for extinction and explores multistability in a second-order Ricker model of stage-structured populations.

Findings

Conditions for global extinction in non-autonomous case

Existence of multistable periodic and non-periodic orbits

Analysis of dynamics in the positive quadrant

Abstract

We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (e.g. adult, juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the non-autonomous case. This gives general conditions for extinction in the biological context. We also study the dynamics of an autonomous special case of the equation that generates multistable periodic and non-periodic orbits in the positive quadrant of the plane.