Periodicity and knots in delay models of population growth

Recently, we investigated the effect of delay on the asymptotic behavior of the model ẋ+x = f (x(·−τ)) of population growth, when the nonlinearity f is a unimodal function. Now we prove that for large delay, there are several nonconstant (positive) periodic solutions. We also use knots theory to study periodic solutions with period 3τ . Some of our results do not rely on the continuity of f and thus are applicable to wider range of biological problems in which the growth functions are piecewise continuous. c © 2007 Elsevier Ltd. All rights reserved.