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Volume 3, Number 1, 2013, Pages 11-20                                                                DOI:10.11948/2013002
Complex dynamics in 2-species predator-prey systems
Ilhem Djellit,Mohamed Lamine Sahari,Amel Hachemi
Keywords:Prey-predator system;Bifurcation basin;Map with denominator;Focal point
Abstract:
      In this work, we consider some dynamical properties and specific contactbifurcations of a discrete-time predator-prey system having inverseswith vanishing denominator. The dynamics is investigated by usingconcepts of focal points, prefocal curves and bifurcation theory.The system undergoes flip bifurcation and Neimark-Sacker bifurcation.Numerical simulations are presented not only to illustrate our resultswith the theoretical analysis, but also to confirm further the complexityof the dynamical behaviors as extinction, persistence and permanence.
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