Prof. Dr. Marat Akhmet,
Middle East Technical University, Turkey
ULTRA POINCARE CHAOS AND SOCIAL SCIENCES
We recently launched an innovative concept in advanced dynamics known as ultra Poincaré chaos. In contrast to conventional conservative methods, this form of chaos is based entirely on the dynamics of a single trajectory. The numerical validation of this behaviour is both reliable and straightforward, making it particularly relevant for effective application in the social sciences. This approach utilizes data gathered from observations and experiments in conjunction with solutions to differential and difference equations. Additionally, we will examine the advantages of this chaotic model in confirming synchronization.
Our discussion will underscore the significance of chaotic models in analysing various domains, including economics, history, politics, and education. We will focus particularly on neural network dynamics, given that brain activity serves as a fundamental basis for all social sciences.
Building on our mathematical findings, we propose new functions designed specifically for modelling time series that have emerged in contemporary research. During our presentation, we will showcase examples of these applications, illustrating how the study of social dynamics—one of the most complex areas—can effectively utilize our insights.
Finally, we will present persuasive arguments underscoring the significance of studying chaos and the presence of thresholds in the history of dynamical systems, particularly in relation to complexity. We will contrast what we refer to as “chaotic” modelling with “industrial” modelling. The relevance of chaotic models for the social sciences is driven by the inherent complexity of the dynamics involved.
