Deterministic dynamics emerging from a cortical functional architecture.

Cerebral cortex has a range of interconnected functional architectures. Some appear random and without structure, while others are geometrical. Although the biological details certainly constrain spatial temporal patterns in neural networks, the influence that the laws of deterministic dynamics bring to bear on even isolated simple geometries are unknown. Layer II/III of primary visual cortex has long range horizontal connections with projections to and from other layers. The long range excitatory connections were modeled in isolation as an isolated laterally connected functional architecture. The Hodgkin-Huxley or Pinsky-Rinzel equations were used to simulate the neuronal elements. Waves of activity could propagate through the functional architecture; depending on the synaptic kinetics, the system could settle down into quiescence, oscillations, or seemingly random behavior. Order could be found in random-looking behavior by the application of techniques from chaos theory. Furthermore, the range and transitions of the temporal patterns in the modeled collection of neurons are similar to those found in other non-linear systems. The possibility that the temporal patterns of neurons in situ are also constrained by these mathematical laws is discussed.