Simulação do comportamento crítico de um modelo de atividade neuronal em uma rede modular hierárquica

Abstract

The study of networks formed by interaction between components of a system has aroused great interest in natural science, particularly in the study of biological systems, including the brain. Real nervous systems are highly inhomogeneous. The hierarchical modular structure of the brain can affect the organization of the neural dynamics, providing an extended parameter range for power-law behavior via a regional mix of sub and supercritical behavior, a phenomenon known as Griffiths phases, in which the critical dynamics of power laws appear on a extended region around the critical point. In this work, we review concepts in neuroscience, critical phenomena and complex networks; we simulate the contact process on a square lattice; and finally, we perform a study of the critical behavior of a brain network with hierarchical modular structure by computer simulations. We calculate some critical exponents of the model by means of finite size scaling theory; we verify evidences of a Griffiths phase.