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Bifurcation analysis of a Kolmogorov type tritrophic model. (English) Zbl 1505.37100

Summary: A tritrophic food chain model of Kolmogorov type is analyzed. The mesopredator and superpredator populations are specialist, the functional responses are general and the prey has general growth rate function. Independently of the functional responses and of the growth rate of the prey, conditions to have the existence of stable limit sets obtained by a Bogdanov-Takens bifurcation are proved. The general results, fixing Holling type functional responses and logistic growth rate for the prey are illustrated. Moreover, derived from our Bogdanov-Takens bifurcation results, the coexistence of the three species by means of stable limit cycles or quasiperiodic orbits with chaotic motion is numerically shown. Finally, general formulae for the second-order homoclinic predictor are computed and numerically illustrated.

MSC:

37N25 Dynamical systems in biology
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
34C60 Qualitative investigation and simulation of ordinary differential equation models
92D25 Population dynamics (general)
92D40 Ecology
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