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Journal of Applied Nonlinear Dynamics 15(2) (2026) 325--334 | DOI:10.5890/JAND.2026.06.005

Jaume Llibre, Leonardo Serantola

$^1$ Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

$^2$ Departamento de Matem'{a}tica, Ibilce--UNESP, 15054-000 S~{a}o Jos'{e} do Rio Preto, Brasil

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Abstract

This paper studies the bifurcation of limit cycles for a specific predator-prey model called Rosenzweig-MacArthur, that presents persistent oscillations in the amount of individuals of the population from predator group and from the prey group. This model uses a Holling Type II function response. The averaging theory of third order allows to investigate the Hopf bifurcation that exhibits this model, providing an analytical approximation of the bifurcated periodic orbit and its kind of stability.

Acknowledgments

The first author has been partially supported by the Agencia Estatal de Investigaci\'on of Spain grant PID2022-136613NB-100, AGAUR (Generalitat de Catalunya) grant 2021SGR00113, and by the Reial Acad\`emia de Ci\`encies i Arts de Barcelona.

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