Expansion of ideas and processes in social and biological communities

Most modern technological, social and information systems can be viewed as a complex system with a set of interacting components. Modeling the interaction of these components is of considerable interest [1–4]. The paper has been investigated the expansion of ideas under different initial conditions. The constructions of analytical solutions the equations allows to determine of the saturation conditions for the solutions which have been founded. The effect of standing waves since the presence of a diffusion term in the equation of cellular automata is founded. In the numerical modeling of the processes of the dissemination of ideas, a fact of "spotting" was found — the grouping (clustering) of agents with the same ideas. For the biological population, the phenomenon of "spotting" was first noticed by A.A. Lyapunov.