Dynamical analysis of a plant–herbivore model with double delay effect and double allee effect

In this study, a plant–herbivore model with double time delays and double Allee effects was constructed, incorporating intraspecific competition among herbivores. Theoretical analyses established the existence conditions of the positive equilibrium point and the boundedness of solutions. The stability and Hopf bifurcation of equilibria in the non-delayed system were thoroughly investigated, and the existence of Hopf bifurcations and global stability under double delays were examined. Numerical simulations demonstrated that when delays exceed critical thresholds, Hopf bifurcations occur, leading to system instability. Double Allee effects were shown to exacerbate this process, with increasing Allee intensity reducing plant population density.