Abstract
The existence conditions of Hopf bifurcation for a predator–prey model based on nutrition kinetics are given. The two results may appear as follows: one is that the model has a stable periodic trajectory from Hopf bifurcation, which shows the system is in an ecological balance; the other is that periodic trajectory from Hopf bifurcation is unstable, which indicates the system is in a sharp or catastrophic loss of stability. For the latter, a bifurcation controller is designed to make the periodic trajectory stable. Finally, some simulations are carried out to prove the results.
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