This article shows the basic tenets of the deterministic chaos theory that brings a new methodological framework and tools for exploring and understanding complex behavior in dynamical systems. We put an emphasis on description of the Verhulst logistic map which is one of the possible models and methods for researching dynamical systems that could develop to chaotic. 

In this paper we decribe the application of Verhulst method in biology, medicine, economy, political and social science, physics, and demography and information science. In the field of information science concepts of chaos theory proved as a valuable support in the research of interactions between information systems and their host organizations.

The pioneer work with Logistic map was made in biology, but today this method is more frequently used in different scientific researces. It was discovered  by the Belgian mathematician Pierre Francois Verhulst in the 1845 in order to describe the change in the population of a biological species.