摘要 : This paper deals with the investigation of the three species food-web model. This model includes two logistically growing interaction species, namely x and y, and the third species z behaves as the predator and also host for x. Th... 展开 This paper deals with the investigation of the three species food-web model. This model includes two logistically growing interaction species, namely x and y, and the third species z behaves as the predator and also host for x. The species z predating on the species y with the Holling type-II functional response, while the first species x is benefited from the third species z. Further, the effect of fear is incorporated in the growth rate of species x due to the predator y and time lag in z due to the gestation process. We explore all the biologically possible equilibrium points, and their local stability is analyzed based on the sample parameters. Next, we investigate the occurrence of Hopf-bifurcation around the interior equilibrium point by taking the value of the fear parameter as a bifurcation parameter for the non-delayed system. Moreover, we verify the local stability and existence of Hopf-bifurcation for the corresponding delayed system. Also, the direction and stability of the bifurcating periodic solutions are determined using the normal form theory and the center manifold theorem. Finally, we perform extensive numerical simulations to support the evidence of our analytical findings. 收起