Initial Condition and Behavior Patterns in Learning Dynamics: Study of Complexity and Sustainability from Time Series

Learning is an essential part of human life. In it, our sensory organs and neural networks participate and integrate emotional behaviors, indagative and persuasive abilities, along with the ability to selectively acquire information, to mention a fraction of the media used in learning, converge to it. This study presents the results of the observational monitoring of behaviors, displayed by teams of students in learning processes, their interactions, representing them as series of time. These time series contain the dynamics of learning: weak, average, and chaotic, differentiated by the control parameter (connectivity) that is increasing respectively. The exponents of Lyapunov, the entropy of Kolmogorov, the complexity, the loss of information for each series, and the projection horizon of the processes are calculated for each series. The results, approximate, show that the chaotic dynamics propitiate the learning, given that there is an increase of connectivity within the teams breaking patterns or behavioral stereotypes. The entropic character of connectivity allows estimating the complexity of this human activity, exposing its sustainability, which brings irreversible conflicts with nature, given that the universe of nonequilibrium is a connected universe. Finally, the analysis model developed is historically contextualized, in first approximation, in some ancient civilizations.