A predator-prey system with generalized Holling type IV functional response and Allee effects in prey

The transition between strong and weak Allee effects in prey provides a simple regime shift in ecology. In this paper, we study the interplay between the functional response of Holling type IV and both strong and weak Allee effects. The model investigated here presents complex dynamics and high codimension bifurcations. In particular, nilpotent cusp singularity of order 3 and degenerate Hopf bifurcation of codimension 3 are completely analyzed. Remarkably it is the first time that three limit cycles are discovered in predator-prey models with multiplicative Allee effects. Moreover, a new unfolding of nilpotent saddle of codimension 3 with a fixed invariant line is discovered and fully developed, and the existence of codimension 2 heteroclinic bifurcation is proven. Our work extends the existing results of predator-prey systems with Allee effects. The bifurcation analysis and diagram allow us to give biological interpretations of predator-prey interactions. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the interaction between Holling type IV functional response and both strong and weak Allee effects, revealing complex dynamics and high codimension bifurcations in the model studied. The discovery of three limit cycles in predator-prey models with multiplicative Allee effects is particularly noteworthy, along with the analysis of nilpotent cusp singularity of order 3 and degenerate Hopf bifurcation of codimension 3. This work extends existing results on predator-prey systems with Allee effects, providing biological interpretations of predator-prey interactions through bifurcation analysis and diagrams.