Application of cellular automata in neuroscience: dynamic models of neuron populations

The collective activity of neurons in cortical circuits enables us to think, perceive, learn and move. Modeling this activity through cellular automata (CA) based approaches provides a common mathematical framework for merging, explaining, testing, and anticipating empirical data. This review introduces the CA applications for the dynamic modeling of neuron populations and brain activity. A non-systematic literature search was conducted on the application of CA in modeling neuron populations and brain activity. This paper emphasizes the dynamics of large-scale networks (e.g., as found in the brain) rather than smaller neuronal systems. Publications were identified with different approaches based on CA that examined various aspects related to the nonlinear dynamic properties of one or more neuronal populations corresponding to brain areas. CA models could yield different dynamics from multistability, including limit-cycle as well as fixed-point attractors, to extremely nonlinear dynamics that produce complex aperiodic nonlinear oscillations. It was also shown that a CA model of neuronal populations could yield self-organized criticality as an essential property of neural systems. By integrating various empirical findings from the microscopic to macroscopic level into a mathematical framework that can be refined iteratively, dynamic CA models are suitable tools to explain and interpret complex neural mechanisms involved in perception and behavior. While important challenges remain, evidence from CA models indicates that collective nonlinear dynamics are the main concepts for adaptive cortical activity.