STABLE POSITIVE PERIODIC-SOLUTION OF TIME-DEPENDENT LOTKA-VOLTERRA PERIODIC MUTUALISTIC SYSTEM

The time dependent Lotka-Volterra mutualistic system x(i) = x(i)(r(i)(t) + SIGMA(j=1)n(alpha)ij(t)x(i)), (i = 1,..., n). be considered under the assumption that r(i)(t) and alpha(ij)(t) are omega-periodic functions. A set Of easily verifiable sufficient conditions are given which gurantee the global asymptotic stability of positive omega-perodic solution of system (1). When r(i)(t), alpha(ij)(t) are constants, the conditions are coincident with the necessary and sufficient condition that the positive equilibrium (if there exists) is global asymptotic stable.