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The conditions to have a stable limit cycle by an Andronov–Hopf bifurcation in a tritrophic model are given. A generalized logistic growth function for the prey is considered, and a general family of functional responses, including the Holling type, are taken for the predators. Some results obtained in previous works for tritrophic models, which consider logistic growth in the prey and Holling functional responses, are generalized.

Limit cycles in a tritrophic food chain model with general functional responses