Abstract
In this paper, a predator–prey model with Holling-II type functional response and a prey refuge is considered. The existence of Hopf bifurcations at the positive fixed point is established by analyzing its distribution of characteristic values. The stability and the directions of Hopf bifurcations of the model are derived for the variation of some crucial parameters. It is shown that these key parameters have a tremendous influence on the coexistence, the oscillation, and the stability of the considered model. Finally, numerical simulations are carried out to illustrate the validity of the results.
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