l Vocational and Technical College, Puyang 457001, China;Р 2. School of mathematics and physics, Anyang University, Anyang 455000, China）РРAbstract: The fractional time-delay predator-prey model with fear effect and prey refuge is studied, and the stability conditions ofРthe model at the coexistence equilibrium point are obtained by the linearization theory of differential equations and numericalРsimulation method. Being taken the time-delay as the bifurcation parameter, the existence of Hopf bifurcation at the coexistenceРequilibrium point of the system is studied. The prediction correction algorithm is used for numerical simulation to verify theРcorrectness of the conclusion.РKeywords: ifractional-order; time-delay; Lyapunov asymptotically stable; Hopf bifurcation
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