Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Geertz, C.: The interpretation of cultures. Library of Congress (1973)
Van Gennep, A.: The Rites of Passage. Psychology Press (2004)
Bohr, N.: Atomic Physics and Human Knowledge. Dover Publications (2010)
Gubanov, D., Petrov, I.: Multidimensional model of opinion polarization in social networks. In: Twelfth International Conference Management of large-scale system development (2019)
Kozitsin, I.V., et al.: Modeling political preferences of Russian users exemplified by the social network Vkontakte. Math. Models Comput. Simul. 12, 185–194 (2020)
Mikhailov, A.P., Petrov, A.P., Proncheva, O.G.: A model of information warfare in a society with a piecewise constant function of the destabilizing impact. Math. Models Comput. Simul. 11, 190–197 (2019)
Lotman, Yu.M.: Semiosphere (in Russian). Art-SPb (2000)
Flache, A., et al.: Models of social influence: towards the next frontiers. J. Artif. Societies, Social Simul. 20(4) (2017)
Mäs, M.: Challenges to simulation validation in the social sciences. a critical rationalist perspective. In: Beisbart, C., Saam, N.J. (eds.) Computer Simulation Validation. SFMA, pp. 857–879. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-70766-2_35
Peralta, A.F., Kertesz, J., Iniguez, G.: Opinion dynamics in social networks: from models to data (2022)
Kozitsin, I.V.: Opinion dynamics of online social network users: a microlevel analysis. J. Artif. Soc. Soc. Simul. 47(1), 1–41 (2021)
Kozitsin, I.V.: A general framework to link theory and empirics in opinion formation models. Sci. Reports. 12(1) (2022)
Mikolov, T., Sutskever, I., Chen, K., Corrado, S. G., Dean, J.: Distributed representations of words and phrases and their compositionality. In: Proceedings of Workshop at ICLR. arXiv:1310.4546 (2013)
Belotelov, N.V., Loginov, F.V.: The agent model of intercultural interactions: the emergence of cultural uncertainties. Comput. Res. Model. 14(5), 1143–1162 (2022)
Belotelov, N.V., Loginov, F.V.: Cross-cultural interactions model. AIP Conf. Proc. 2425(1), 420030 (2022). https://doi.org/10.1063/5.0081727
DeGroot, M.: Reaching a consensus. J. Am. Stat. Assoc. 69(345), 118–121 (1974). https://doi.org/10.2307/2285509
Jackson, M.O.: Social and Economic Networks. Princeton University Press (2008)
Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Nauka, Moscow. (in Russian), pp. 464–465 (1989)
Burago, D., Burago, Y., Ivanov, S.: A Course in metric geometry. Rhode Island: American Mathematical Society Providence, Example 1.2.25. (2001)
Chandler, D.: The norm of the Schur product operation. Numer. Math. 4, 343–344 (1962)
Belotelov, N.V., Loginov, F.V.: Agent-based approach of cross-cultural interactions in hilbert space. Proc. Future Technol. Conf. 2021(1), 252–263 (2022)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Belotelov, N., Loginov, F. (2024). Agent-Based Model of Cultural Landscape Evolution in Euclidean Space. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V. (eds) Advances in Optimization and Applications. OPTIMA 2023. Communications in Computer and Information Science, vol 1913. Springer, Cham. https://doi.org/10.1007/978-3-031-48751-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-031-48751-4_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-48750-7
Online ISBN: 978-3-031-48751-4
eBook Packages: Computer ScienceComputer Science (R0)