Journal of the
Korean Mathematical Society JKMS

The present paper is concerned with a two-competitor/one-prey population system with Holling type-II functional response and two discrete delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are investigated. Particularly, by applying the normal form theory and the center manifold reduction for functional differential equations (FDEs), explicit formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are derived. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.

Keywords: three-species system, time delays, bifurcation, stability, periodic solution

MSC numbers: 34K13, 37G05, 37G15, 92D25