Nonlinear interdependence in neural systems: Motivation, theory, and relevance

In this article, we motivate models of medium to large-scale neural activity that place an emphasis on the modular nature of neocortical organization and discuss the occurrence of nonlinear interdependence in such models. On the basis of their functional, anatomical, and physiological properties, it is argued that cortical columns may be treated as the basic dynamical modules of cortical systems. Coupling between these columns is introduced to represent sparse long-range cortical connectivity. Thus, neocortical activity can be modeled as an array of weakly coupled dynamical subsystems. The behavior of such systems is represented by dynamical attractors, which may be fixed point, limit cycle, or chaotic in nature. If all the subsystems are perfectly identical, then the state of identical chaotic synchronization is a possible attractor for the array. Following the introduction of parameter variation across the array, such a state is not possible, although two other important nonlinear interdependences-generalized and phase synchronized-are possible. We suggest that an understanding of nonlinear interdependence may assist advances in models of neural activity and neuroscience time series analysis.