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Deterministic dynamics emerging from a cortical functional architecture.

R M Siegel1, H L Read

  • 1Center for Molecular and Behavioral Neuroscience, Rutgers University, Newark, NJ 07102, USA. axon@cortex.rutgers.edu

Neural Networks : the Official Journal of the International Neural Network Society
|October 23, 2001
PubMed
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Deterministic dynamics may govern neural activity patterns in the cerebral cortex. Mathematical laws, including chaos theory, can reveal order in seemingly random neuronal network behavior.

Area of Science:

  • Computational neuroscience
  • Theoretical neuroscience
  • Systems neuroscience

Background:

  • The cerebral cortex exhibits diverse functional architectures, some geometrical and others appearing random.
  • The influence of deterministic dynamics on neural network spatial-temporal patterns, particularly in simple geometries, remains largely unknown.
  • Layer II/III of the primary visual cortex features long-range horizontal connections.

Purpose of the Study:

  • To model long-range excitatory connections in the primary visual cortex in isolation.
  • To investigate the potential role of deterministic dynamics and chaos theory in shaping neuronal activity patterns.
  • To explore the relationship between neuronal temporal patterns and non-linear systems.

Main Methods:

  • Simulated neuronal elements using the Hodgkin-Huxley or Pinsky-Rinzel equations.

Related Experiment Videos

  • Modeled isolated, laterally connected functional architectures representing long-range horizontal connections.
  • Applied techniques from chaos theory to analyze neuronal behavior.

    • Main Results:

    • Propagating waves of activity were observed within the modeled functional architecture.
    • The system exhibited diverse behaviors including quiescence, oscillations, and seemingly random activity, dependent on synaptic kinetics.
    • Analysis revealed order within random-looking neuronal activity patterns using chaos theory.

    Conclusions:

    • The temporal patterns of neuronal networks may be constrained by mathematical laws, similar to other non-linear systems.
    • Deterministic dynamics and chaos theory offer a framework for understanding complex neuronal behaviors.
    • Further investigation is warranted to explore these mathematical constraints on in situ neuronal activity.