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Entrainment control in a noisy neural system.

Diek W Wheeler1, W C Schieve

  • 1Physics Department, The University of Texas, Austin, Texas 78712, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
Summary

This study applies open-plus-closed-loop (OPCL) entrainment control to effective-neuron systems, successfully extracting stable limit cycles from chaos. Moderate noise levels did not hinder this memory retrieval-like process.

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Area of Science:

  • Dynamical Systems
  • Computational Neuroscience
  • Nonlinear Dynamics

Background:

  • The open-plus-closed-loop (OPCL) entrainment control method is a technique for stabilizing desired dynamics within a system.
  • Chaotic attractors represent complex, unpredictable system states, analogous to memory searching states.
  • Effective-neuron systems are simplified models used to study neural dynamics.

Purpose of the Study:

  • To apply the OPCL entrainment control to an effective-neuron system.
  • To investigate the extraction of stable limit cycles from chaotic attractors using OPCL control.
  • To assess the impact of additive Gaussian white noise on the entrainment process.

Main Methods:

  • Implementation of the OPCL entrainment control algorithm on an effective-neuron model.
  • Introduction of additive Gaussian white noise to the system.
  • Analysis of system behavior using phase-space plots and Lyapunov exponents.

Main Results:

  • Stable limit cycles were successfully extracted from a chaotic attractor in the effective-neuron system.
  • Moderate levels of additive Gaussian white noise showed minimal negative impact on the entrainment process.
  • Phase-space plots and negative Lyapunov exponents indicated successful stabilization and synchronization.

Conclusions:

  • OPCL entrainment control is effective in extracting stable limit cycles from chaotic attractors in effective-neuron systems.
  • The control method demonstrates robustness against moderate levels of natural system noise.
  • The observed negative Lyapunov exponents suggest a strong connection between OPCL control and chaotic synchronization phenomena.

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