Periodicity in a food-limited population model with toxicants and state dependent delays

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 food-limited population model with toxicant and state dependent delays, that is du(t)/dt = u(t) {r(t) - a(t)u(t) - Sigma(j=1)(m) b(j)(t)u(t - tau(j)(t,u(t)))/k(t) + c(t)u(t) + Sigma(j=1)(m) d(j)(t)u(t - eta(j)(t,u(t)))}, where r(t), k(t), a(t), b(j)(t), d(j)(t), j = 1,2,...,m, are continuous, real-valued periodic functions with period omega > 0 and r(t), k(t), a (t) > 0; b(j)(t), d(j) (t) greater than or equal to 0, j = 1, 2,..., m, are periodic continuous functions with period omega > 0, tau(j), eta(j) are omega-periodic with respect to their first arguments. Some new results are obtained. (C) 2003 Elsevier Inc. All rights reserved.