"Heterogeneity and Criticality in Neural Networks: A Computational Model of the Griffiths Phase"

Abstract

This article presents a computational exploration into the dynamics of neural networks, focusing on the manifestation of heterogeneity and critical behavior akin to the Griffiths phase observed in condensed matter physics. Drawing inspiration from the rich tapestry of neural activities within the human neocortex, we develop a simplified model to investigate how networks with diverse propensities for critical behavior can exhibit complex, adaptive functionalities. Utilizing an Erdős–Rényi random graph as the foundation, we introduce a proportion of nodes designated as "critical," possessing a higher likelihood of activation, to simulate the nuanced interplay between different regions of a theoretical brain network. Through iterative simulations, we examine the activation patterns over time, paying close attention to the influence of critical nodes on the overall network dynamics. The model integrates fundamental principles from network theory and neuroscience, offering insights into the potential mechanisms underlying the brain's remarkable ability to process information efficiently, adapt to new stimuli, and maintain robustness in the face of perturbations. Our findings highlight the importance of heterogeneity and criticality in enhancing the computational capabilities of neural networks, providing a conceptual bridge between theoretical physics and cognitive neuroscience. This work contributes to a deeper understanding of the brain's operational principles and opens avenues for further research into the applications of criticality and Griffiths phases in artificial intelligence and neural network design.