Allee effects in a Ricker-type predator-prey system

TL;DR

This paper investigates how Allee effects influence the dynamics of a discrete host-parasitoid system modeled with a Ricker-type host population, analyzing stability and basins of attraction for various growth rates.

Contribution

It provides a detailed analysis of stability and basins of attraction in a host-parasitoid model incorporating Allee effects and Ricker dynamics, including conditions for multiple steady states.

Findings

Existence and stability of interior steady states depend on host growth rate.

Basins of attraction are characterized for different parameter regimes.

Multiple interior steady states can occur with high host growth rates.

Abstract

We study a discrete host-parasitoid system where the host population follows the classical Ricker functional form and is also subject to Allee effects. We determine basins of attraction of the local attractors of the single population model when the host intrinsic growth rate is not large. In this situation, existence and local stability of the interior steady states for the host-parasitoid interaction are completely analyzed. If the host's intrinsic growth rate is large, then the interaction may support multiple interior steady states. Linear stability of these steady states is provided.