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A two species Lotka-Volterra competitive system with infinite delays and single feedback control variable is studied. Sufficient conditions which ensure the extinction and global stability of the system are obtained, respectively. Our extinction result shows that for the traditional Lotka-Volterra competitive system, in any one of the cases: (i) globally stable, (ii) extinct and (iii) bistable, by choosing the suitable feedback control variable, one of the species will be driven to extinction, while the other one will stabilize at a positive equilibrium. Specially, by choosing the suitable feedback control variable, the extinct species in original system could become permanent, while the permanent species in original system will be driven to extinction. Our stability result shows that under certain conditions, the extinct species can become globally stable and the stable species still keep the property of stability.
How to Cite this Article:
Fengde Chen, Haina Wang, Dynamic behaviors of a Lotka-Volterra competitive system with infinite delays and single feedback control, Journal of Nonlinear Functional Analysis 2016 (2016), Article ID 43.