Sensitivity of certain dynamic systems with respect to a small delay

A class of nonlinear differential equations of order one with pure delay is examined. It is found that the 'effective' order of an equation of this class need not be constant for all values of the delay parameter, even if the latter is small. In the autonomous case periodic solutions are determined and the domain of influence of a constant steady state is estimated. In the non-autonomous case the periodic and almost periodic solutions are of more varied types than for analogous differential equations without pure delay. (34 refs).