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Stability and Neimark-Sacker bifurcation of a ratio-dependence predator-prey model. (English) Zbl 1369.39011
Summary: In this paper, stability and bifurcation of a two-dimensional ratio-dependence predator-prey model has been studied in the close first quadrant $$\mathbb R^2_+$$. It is proved that the model undergoes a period-doubling bifurcation in a small neighborhood of a boundary equilibrium and moreover, Neimark-Sacker bifurcation occurs at a unique positive equilibrium. We study the Neimark-Sacker bifurcation at unique positive equilibrium by choosing $$b$$ as a bifurcation parameter. Some numerical simulations are presented to illustrate the theoretical results.

##### MSC:
 39A28 Bifurcation theory for difference equations 39A30 Stability theory for difference equations 92D25 Population dynamics (general) 65Q10 Numerical methods for difference equations
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