Complexity in Dynamic Academic Systems from Topology and Genetic Grammars

This chapter sheds a new light on the theoretical foundations of the main contemporary initiatives towards the adequacy of the teaching-learning process to the great changes of our society. An academic environment can evolve from chaos to stabilised states, and this theoretical study will present and also discuss a chaotic simulation model that addresses this. This study will provide a consistent foundation for new methodological initiatives that support shifts in the traditional paradigm of education and learning.

The study was designed from the classical literature on chaotic systems with some original theoretical implementations.

This study is based on the configuration of a DAS toy model by means of computational simulations carried out on a virtually built random academic environment. The individuals were classified by profiles of ordered abilities represented by binary strings defining a topology. Such topology fixed the type of the strings and their transcriptions to decimal system. To simulate the evolution of the system, three differential equations were numerically combined in convolution, one of which made reference to those strings transformed into decimal signatures. The simulations were run using the Maple and R programming languages.

Simulations showed attractors for different time intervals of iterations. For wide ranges of individual propensities to develop the six abilities described in the work it was observed that the dissimilarities of individual profiles induced attractors with narrow boundaries. Growing the number of individuals, this tendency was maintained.

The study displayed simulations of academic systems made up of professors and researchers interacting in a stable environment, highlighting how these systems could transition from chaotic configurations to stability and produce well-defined attractors.