Dynamical behaviour of a Lotka–Volterra competitive-competitive–cooperative model with feedback controls and time delays

The aim of this paper is to investigate the dynamical behaviour of a class of three species Lotka–Volterra competitive-competitive–cooperative models with feedback controls and time delays. By developing a new analysis technique, we obtain some sufficient conditions that ensure these models have the dynamical property of permanence. We also give some sufficient conditions that guarantee the global attractivity of positive solutions for this system by constructing a new suitable Lyapunov function. Finally, we give some numerical simulations to illustrate our results in this paper