Oscillations and coexistence generated by discrete delays in a two-species competition model

One of the shortcomings of the classical Lotka-Volterra competition model is that both species' births are assumed to be instantaneous, whereas developmental and maturation processes may cause time delays. We extend the Lotka-Volterra competition model to a delayed model based on a single species delayed model in this paper. The effects of two discrete delays on competition outcomes are investigated. Our theoretical and numerical results show that delays can cause the loss of stability of equilibria and the emergence of periodic solutions (i.e., population density oscillations) via Hopf bifurcation, lead to exclusion by changing the stability of coexistence equilibrium, and boost coexistence even if the coexistence equilibrium point does not exist.