Stability and Neimark–Sacker bifurcation of a ratio‐dependence predator–prey model |
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| Authors: | Abdul Qadeer Khan |
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| Institution: | Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, Pakistan |
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| Abstract: | In this paper, stability and bifurcation of a two‐dimensional ratio‐dependence predator–prey model has been studied in the close first quadrant  . 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 theocratical results. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | ratio‐dependence model local stability Neimark– Sacker bifurcation bifurcation theory subclass 39A10 40A05 |
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. 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 theocratical results. Copyright © 2017 John Wiley & Sons, Ltd.