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Abstract
By the techniques of comparison argument and Lyapunov-like functionals, some criteria about persistence and extinction of the species are obtained. And then, with the help of constructing Lyapunov functionals and some new analysis method, sufficient conditions, provided with the form of average value of a function, to guarantee the stability of the system are derived. Finally, some examples together with their numerical simulations show the feasibility of these main results. Our conclusions are different from many existing forms for nonlinear competitive systems.
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