Periodicity and knots in delay models of population growth

Recently, we investigated the effect of delay on the asymptotic behavior of the model x ̇ + 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 3 τ . 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.