Complex dynamics in a singularly perturbed Hastings–Powell model with the additive Allee effect

In this article, we investigate the complex dynamics of the Hastings–Powell model with the additive Allee effect. Due to the differences of each species at different time scales, we establish a three-time scale model to describe the rate of change of species, dividing into fast, intermediate, and slow, through the scale transformation of parameters and variables. Based on geometric singular perturbation theory and Shilnikov bifurcation theory, we show the existence of periodic orbits and Shilnikov-type chaos. In addition, with the help of numerical simulation, we find that the severity of the additive Allee effect can weaken phenomena such as oscillation and chaos.