Influence of single feedback control variable on an autonomous Holling-II type cooperative system

An autonomous two-species Holling-II type cooperative system with single feedback control is considered in this paper. Firstly, by applying the comparison theorem of differential equation, sufficient conditions which ensure the permanence of the system are obtained. Secondly, by constructing some suitable Lyapunov function and using the average Inequality, some sufficient conditions for the globally asymptotical stability and extinction of the system are obtained. Our results show that by choosing suitable values of feedback control variables, stable species could become extinct, or still keep the property of globally stable.