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Stability and Hopf Bifurcations of a Three-Species Symbiosis Model with Delays

In this paper, a three-species symbiosis Lotka–Volterra model with discrete delays is considered. The stability of positive equilibrium and the existence of Hopf bifurcations are investigated firstly and then the direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem.