Dynamical analysis in an exploited two-species competition model with double time delays

In this paper, a mathematical model is established to investigate interaction and coexistence mechanism of two-species competition ecosystem with nonlinear intraspecific regulation. The combined dynamic effects of maturation delay and harvest effort on population dynamics are discussed. Conditions for existence of unique interior equilibrium are investigated. Positivity and boundedness of solutions are analytically studied. By analyzing associated characteristic equation, local stability of the proposed model around the interior equilibrium is discussed. Furthermore, by constructing an appropriate Lyapunov functional, global stability of the unique interior equilibrium is discussed. Numerical simulations are carried out to show consistency with theoretical analysis.