Agraïments: The first author is partially supported by an ANR grant "Analyse non linéaire et applications aux rythmes du vivant BLAN07-2-182920

Françoise, Jean-Pierre

Llibre, Jaume

International audienceWe provide an analytical proof of the existence of a stable periodic orbit contained in the region of coexistence of the three species of a tritrophic chain. The method used consists in analyzing a triple Hopf bifurcation. For some values of the parameters three limit cycles born via this bifurcation. One is contained in the plane where the top-predator is absent. Another one is not contained in the domain of interest where all variables are positive. The third one is contained where the three species coexist. The techniques for proving these results have been introduced in previous articles by the second author and are based on the averaging theory of second-order. Existence of this triple Hopf bifurcation has been previously discovered numerically by Kooij et al

Analytical study of a higher-order Hopf bifurcation in a tritrophic food chain model

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