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Bifurcations and Limit Cycle in the System of Rinaldi-Muratori

N. Mehidi, N. Mohdeb

Abstract


We consider a slow-fast prey-predator model. The existence of a limit cycle in the system is already shown by N. Mehidi. In this work, we give two other proofs using, the Poincré-Bendixson theorem and the Hopf bifurcation one. The variation of only one of the parameters of the system, produces a Hopf and a transcritical bifurcations which we study.

Keywords


Slow-fast system, limit cycle, bifurcation

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