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 foodlimited population model with toxicant and state dependent delays, that is du(t) dt = u(t ) r(t)− a(t)u(t)− m j=1 bj (t)u(t − τj (t ,u(t ))) k(t)+ c(t)u(t)+ m j=1 dj (t)u(t − ηj (t ,u(t ))) , where r(t ), k(t ), a(t ), bj (t ), dj (t ), j = 1, 2, . . .,m, are continuous, real-valued periodic functions with period ω>0 and r(t ), k(t ), a(t )> 0; bj (t ), dj (t ) 0, j = 1, 2, . . .,m, are periodic continuous functions with period ω >0, τj ,ηj are ω-periodic with respect to their first arguments. Some new results are obtained.  2003 Elsevier Inc. All rights reserved