Sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a neutral model with periodic delays and feedback control {(dn/dt = n(t)[a(t) - beta(t)n(t) - Sigmai=1nbi(t)n(t - taui(t)) - Sigmai=1nci(t)n'(t - gammai(t)) - delta(t)u(t) - Sigmai=1ndi(t)u(t - sigmai(t))],)(du/dt = -e(t)u(t) + f(t)n(t) + Sigmai=1ngi(t)n(t - etai(t)).) Our results extend and improve existing results, and have further applications in population dynamics. (C) 2003 Elsevier Inc. All rights reserved.