Fear suppressing chaos in intraguild predation systems

Intraguild predation (IGP) systems, characterized by intertwined predation and competition interactions, exhibit complex ecological dynamics including chaotic behavior. The traditional studies have mainly focused on direct interactions among species and the indirect effects, such as fear-induced responses, have often been overlooked despite their potential to significantly alter food web dynamics. In this study, an IGP model incorporating fear effects is developed based on Holling’s time budget theory, where fear affects both population growth and predation behavior. Through qualitative analysis, sufficient criteria are established for the existence and stability of equilibria and the transcritical bifurcation and Hopf bifurcation are well investigated. Extensive numerical simulations reveal rich dynamical behaviors, including periodic oscillations, chaos and bistability. Notably, the results demonstrate that fear effects can suppress chaotic dynamics: increasing the fear of bottom prey toward middle predator and the fear of middle predator toward top predator can stabilize the IGP system, while the fear of bottom prey toward top predator lacks this stabilizing effect.