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

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Listed:
  • Blé, Gamaliel
  • Guzmán-Arellano, Claudia Isabel
  • Loreto-Hernández, Iván

Abstract

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.

Suggested Citation

  • Blé, Gamaliel & Guzmán-Arellano, Claudia Isabel & Loreto-Hernández, Iván, 2021. "Coexistence in a four-species food web model with general functional responses," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921009097
    DOI: 10.1016/j.chaos.2021.111555
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    References listed on IDEAS

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    1. Huayong Zhang & Ju Kang & Tousheng Huang & Xuebing Cong & Shengnan Ma & Hai Huang, 2018. "Hopf Bifurcation, Hopf-Hopf Bifurcation, and Period-Doubling Bifurcation in a Four-Species Food Web," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-21, September.
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