A note on the periodicities in the logistic analyses of growth processes

In real life growth processes there is always an intrinsic finite response time. This means that these systems do not respond instantaneously so that the logistic modeling of such processes should be formally described by a delayed logistic equation. This poses enormous difficulties to their time evolution modeling as there are no analytical solutions to the delayed logistic equation. In this paper we show that by performing a conventional Verhulst logistic modeling of the corresponding time series data, associated with a fine-coarse analysis of the resulting residuals, we can disclose the underlying periodicities due to the finite time response effects.