A population model is investigated using bifurcation analysis with a bifurcation parameter fear factor in-corporated in prey. Theoretical analysis confirmed that the fear effect can cause various types of local bifurcation. Numerical simulations demonstrate the complex nature of the dynamics,including the coexistence of bistability, pe-riodic oscillations and the extinction of the population. The results demonstrate that the fear effect plays an impor-tant role in the stability of population systems.
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