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

Authors:
Wan-Tong Li;Lin-Lin Wang
Affiliations:
Department of Mathematics, Lanzhou University, Lanzhou Gansu, 730000, People's Republic of China;Department of Applied Mathematics, Tianjing University, Tianjing, 300072, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

Sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with feedback controldxdt=-b(t)x(t)+F(t,x(t-@t"1(t)),...,x(t-@t"n(t)),u(t-@d(t))),dudt=-@h(t)u(t)+a(t)x(t-@s(t)).The method involves the application of Krasnoselskii's 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.