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

Department of Mathematics, Northeast Forestry University Harbin 150040, Heilongjiang, China

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 31 May 2025
Accepted: 19 February 2026

Abstract

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.