Coexistence in a four-species food web model with general functional responses

• Published in: Chaos, solitons and fractals solitons and fractals, 2021-12, Vol.153, p.111555, Article 111555
• Main Authors: Blé, Gamaliel, Guzmán-Arellano, Claudia Isabel, Loreto-Hernández, Iván
• Format: Article
• Language: English
• Subjects: Andronov-Hopf bifurcation; Hopf-Hopf bifurcation; Intraguild predation model; Invariant torus; Limit cycle
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2021.111555

•We analyze the dynamics of an intraguild predation system, considering four species.•We give parameter conditions for the coexistence in the intraguild predation system.•We prove that the system exhibits Andronov-Hopf and Hopf-Hopf bifurcations.•We generalized previous results obtained for intraguild predation systems.•Numerical simulations show different limit sets in the system. The dynamics of an intraguild predation system is analyzed. Two shared resources, a middle predator and a top predator are considered in the model. Parameter conditions for coexistence in the intraguild system are given. The coexistence of species, through the existence of an equilibrium point or a stable limit cycle or an invariant torus is shown. Conditions to have Andronov-Hopf and Hopf-Hopf bifurcation are given. Then, limit sets and complex dynamical behaviors, can exhibit in the system. For a wide family of functional responses, these results are valid. Numerical simulations with varied functional responses are given and different limit sets are shown.