Bachelor’s thesis in Physics: “Dynamics and Structure in Adaptive Neural Networks”
National University of Rosario (UNR), Faculty of Exact Sciences, Engineering and Surveying (FCEIA)
, 2023
A connectome is a map of the connections between neurons in the brain, and the production and study of connectomes is known as connectomics. This can be modeled using an adaptive neural network to analyze the relationship between network structure and node dynamics. The microscopic units of the model are dynamical nodes representing neuronal activity, whose interactions give rise to complex network structures. Links between nodes are selected through an adaptive algorithm that connects dynamical elements with similar internal states. The objective of this work was to study the temporal evolution of the network across different phases while varying parameters such as the coupling factor between nodes and the average number of links per node, obtaining an original result based on the model of Gong and Van Leeuwen. Their work was motivated by the need to understand how biological systems, such as neural networks, can evolve toward a small-world network structure even when their individual components (i.e., nodes) exhibit chaotic dynamics. It has important implications for understanding how biological systems can develop small-world organization and how neural networks may remain efficient at information processing despite chaotic dynamics at the level of individual neurons. To address this question, Gong and Van Leeuwen developed a mathematical model of a neural network with chaotic nodes and subjected the network to a selection process based on its ability to process information. They found that, over time, the network evolved toward a small-world structure, allowing information to propagate efficiently despite the chaotic dynamics of individual nodes. To achieve the objectives of this thesis, numerical simulations were carried out implementing both the individual node dynamics and their interactions through the network, together with functions and parameters used to quantify the network state. The initial goal was to reproduce results reported in previous studies using chaotic maps and specific dynamical mechanisms. Once these results were replicated, the focus shifted to a deeper analysis of a phase transition identified by Gong and Van Leeuwen, incorporating new parameters and additional analyses to characterize the two existing phases as well as the critical transition point.