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 ff 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 3τ3τ. Some of our results do not rely on the continuity of ff and thus are applicable to wider range of biological problems in which the growth functions are piecewise continuous.