Stability results for a hierarchical size-structured population model with distributed delay

TL;DR

This paper analyzes a hierarchical size-structured population model with distributed delay, examining stability through spectral methods, and supports findings with numerical simulations.

Contribution

It introduces a stability analysis framework for a complex population model with hierarchical and nonlinear features, using spectral methods and a novel reproduction function.

Findings

Derived linear stability criteria for the model

Established conditions for population stability

Validated results with numerical simulations

Abstract

In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble competition, while fertility is affected by contest competition. In particular, we assume that there is a hierarchical structure in the population, which affects mating success. The dynamical behavior of the model is analysed via linearisation by means of semigroup and spectral methods. In particular, we introduce a reproduction function and use it to derive linear stability criteria for our model. Further we present numerical simulations to underpin the stability results we obtained.