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Stability and Hopf bifurcations in a competitive Lotka–Volterra system with two delays. (English) Zbl 1067.34075

Summary: We consider a Lotka-Volterra competition system with two delays. We first investigate the stability of the positive equilibrium and the existence of Hopf bifurcations, and then using the normal form theory and center manifold argument, derive explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions.

MSC:

34K18 Bifurcation theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
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