Agent-Based Model of Cultural Landscape Evolution in Euclidean Space

The cultural landscape determines the cultural agent’s diversity. It is believed that the cultures space can be represented as a Hilbert space, in which certain sub-spaces - cultural cones -correspond to different cultures. This allows the agents state to be described by a vector in Hilbert space in the first part of the article and in Euclidean space in the second. The numbers of agents belonging to certain cultures are determined by demographic processes and the educational process, as well as the intensity of intercultural contacts. Interaction between agents occurs within clusters, into which the entire set of agents is divided according to certain criteria. During interaction between agents according to a certain algorithm, the length and angle characterizing the state of the agent changes. It is believed that in the process of intercultural interactions, agents leave their pure cultural cones and form intercultural clusters that do not completely belong to any culture. The mathematical formalization of this process is presented in the first part of the article. We suppose that in such clusters as we described the interaction of agents occurs. The second part of the work is devoted to describing the dynamics of this process. In which the Kolmogorov equations were obtained. These equations describe changes in cultural diversity within these clusters.