Bifurcation analysis in a delayed Lokta–Volterra predator–prey model with two delays

In this paper, a class of delayed Lokta–Volterra predator–prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also provided. Finally, main conclusions are given.

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