Existence and global attractivity of positive periodic solutions of functional differential equations with feedback control

Sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with feedback control d x d t = - b ( t ) x ( t ) + F ( t , x ( t - τ 1 ( t ) ) , … , x ( t - τ n ( t ) ) , u ( t - δ ( t ) ) ) , d u d t = - η ( t ) u ( t ) + a ( t ) x ( t - σ ( t ) ) . The method involves the application of Krasnoselskiiʹs fixed point theorem and estimates of uniform upper and lower bounds of solutions. When these results are applied to some special delay population models with multiple delays, some new results are obtained and some known results are generalized.