Формула Дрейка описывает существенно равновесную ситуацию в популяции коммуникативных цивилизаций (КЦ) Галактики, но не описывает динамические процессы, которые могут иметь место. В статье развивается и обсуждается линейный и нелинейный популяционный анализ, обобщающий формулу Дрейка.

The Drake equation pertains to the essentially equilibrium situation in a population of communicative civilizations (CCs) of the Galaxy, but it does not describe dynamical processes which can occur in it. The linear dynamical theory proposed in the paper is a simplest generalization of the Drake equation. An analysis based on real astrophysical data about star formation rate and on the linear dynamical theory predicts the existence of linear demographic waves in the Galaxy related to the maximum in the star-formation rate about five billion years ago and (possibly) to the origin of life in the Galaxy. The linear theory does not allow for the effect CCs have on each other. The non-linear theory that is also developed in the paper is a further generalization of the Drake equation. Non-linear theory allows for influence of CCs on each other by communication channels. It predicts important phenomena of a sharp phase transition from the "era of silence" to the "era of communication" in the Galaxy and of a bi-stability in the CC population in the relation to the probability of communication as a function of CC formation rate. Possible consequence is a possibility of existence of a very stable self-sustaining state of the CC population with high probability of communication for each CC after the phase transition. The problem is posed: is the Galaxy now in the state before the phase transition to the era of communication or after it? This problem discussed in the relation with the Fermi paradox.