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Stability and Neimark–Sacker bifurcation of a ratio‐dependence predator–prey model
Author(s) -
Khan Abdul Qadeer
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4290
Subject(s) - mathematics , bifurcation , saddle node bifurcation , transcritical bifurcation , bifurcation diagram , period doubling bifurcation , bogdanov–takens bifurcation , infinite period bifurcation , mathematical analysis , nonlinear system , physics , quantum mechanics
In this paper, stability and bifurcation of a two‐dimensional ratio‐dependence predator–prey model has been studied in the close first quadrantR + 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 theocratical results. Copyright © 2017 John Wiley & Sons, Ltd.