• A Polycycle and Limit Cycles in a Non-Differentiable Predator-Prey Model

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      https://www.ias.ac.in/article/fulltext/pmsc/117/02/0219-0231

    • Keywords

       

      Stability; limit cycles; bifurcations; predator-prey model.

    • 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.

    • Author Affiliations

       

      E Sáez1 I Szántó1

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

       
  • Proceedings – Mathematical Sciences | News

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