Global dynamics of a two-stage social insect model incorporating nonlinear egg cannibalism

Abstract

This study refines the two-stage social insect model of Kang et al. (2015) by incorporating a nonlinear egg cannibalism rate. The introduction of nonlinearity presents analytical challenges, addressed through the application of the compound matrix method to rigorously establish global stability. The analysis reveals complex dynamical behaviors, including two distinct types of bistability: one between extinction and coexistence equilibria, and another between low-density and high-density coexistence equilibria. These findings underscore the ecological importance of nonlinear egg cannibalism in shaping population dynamics and enhancing species persistence under resource-limited conditions.