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A polycycle and limit cycles in a non-differentiable predator-prey model

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Abstract

For a non-differentiable predator-prey model, we establish conditions for the existence of a heteroclinic orbit which is part of one contractive polycycle and for some values of the parameters, we prove that the heteroclinic orbit is broken and generates a stable limit cycle. In addition, in the parameter space, we prove that there exists a curve such that the unique singularity in the realistic quadrant of the predator-prey model is a weak focus of order two and by Hopf bifurcations we can have at most two small amplitude limit cycles.

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  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla, 110-V, Valparaíso, Chile

    E. Sáez & I. Szántó

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  1. E. Sáez
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  2. I. Szántó
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Sáez, E., Szántó, I. A polycycle and limit cycles in a non-differentiable predator-prey model. Proc Math Sci 117, 219–231 (2007). https://doi.org/10.1007/s12044-007-0018-9

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  • DOI: https://doi.org/10.1007/s12044-007-0018-9

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