Modelling and analysis of population dynamics using Lur’e systems accounting for competition from adult conspecifics

We study the equilibrium dynamics of a Lur’e system modelling a structured population, where adult conspecifics are assumed to have a negative density-dependent feedback on the recruitment of possible recruits. We find that, depending on the model’s parameter values, the population either goes extinct or has a positive equilibrium that is asymptotically stable, globally attracting or globally asymptotically stable. We apply our results to an integral projection model for the Platte thistle (Cirsium canescens) and highlight open aspects of this problem for future work.