Discoveries with Hierarchy of Mean-Field Models of Cellular Automaton

The brain is a complex, far-from-equilibrium dynamical system consisting of diverse populations of neurons and neurotransmitters. The high complexity of brains makes it nearly impossible to understand the underlying mechanisms at play when considering every component. To gain an understanding of the brain we use a stochastic cellular automata archetype called the Generalized Cortical Branching Model(GCBM) to simulate the activity of excitatory and inhibitory neurons with various interactions between the neurons. The GCBM is a finite grid of neurons with activity states of quiescent, active, and refractory. They interact with the nearest neighbors following an updating rule with a stochastic component. This model is not analytically tractable but we can use a hierarchy of mean-field theory models which is analytically tractable which allows for understanding and predictability within the many-body model. Doing so allows us to understand phase transitions with inhibitory effects, maximum susceptibility, mean-field critical exponents, chaotic dynamics of the system, and periodicity of the system(quasi-periodicity) due to driving inhibitory neurons.