The effects of two discrete delays on the competition outcomes in a Beverton-Holt competition model

In this paper, we develop and study a Beverton-Holt competition model incorporating two discrete time delays. We establish the existence, uniqueness, and boundedness of solutions. We analyze the stability of equilibrium points under the influence of the delays. Our primary focus is on understanding the impact of these two delays on competition outcomes and species population abundances. Our theoretical and numerical results reveal that delays can destabilize equilibrium states, leading to the emergence of periodic solutions (i.e., population density oscillations) through Hopf bifurcation. Our findings suggest that sufficiently large delays can alter the competition outcome, shifting from species coexistence to the exclusion of one species.