Bifurcations in a discrete-time Beddington–DeAngelis prey–predator model with fear effect, prey refuge and harvesting

This paper considers a discrete-time Beddington–DeAngelis prey–predator model with fear effect, prey refuge and harvesting. We first establish the existence and local stability of equilibria for the model. Two codimension-one bifurcations (fold and transcritical) and four codimension-two bifurcations (1:1, 1:2, 1:3 strong resonance and fold–flip) are investigated by employing the center manifold theorem and bifurcation theory. We also give the corresponding bifurcation diagrams, phase portraits and diagrams of maximum Lyapunov exponents to verify our theoretical analysis. Besides, we provide some numerical analysis of initial conditions and two-parameter spaces.