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Attractors in continuous and Boolean networks.

Johannes Norrell1, Björn Samuelsson, Joshua E S Socolar

  • 1Physics Department and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
PubMed
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Boolean networks approximate continuous dynamical systems. Reliable Boolean attractors match stable continuous attractors in simple rings, but complex logic introduces non-Boolean dynamics.

Area of Science:

  • Dynamical Systems Theory
  • Boolean Networks
  • Computational Neuroscience

Background:

  • Continuous dynamical systems are often modeled using Boolean networks.
  • Understanding the relationship between continuous and Boolean attractors is crucial for accurate modeling.

Purpose of the Study:

  • To determine which Boolean attractors accurately approximate attractors in continuous dynamical systems.
  • To investigate the dynamics of Boolean networks in simple and complex configurations.

Main Methods:

  • Analysis of switching characteristics in continuous systems.
  • Examination of pulse propagation within network structures.
  • Comparison of Boolean attractor stability with continuous system attractors.

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Main Results:

  • For simple ring networks, "reliable" Boolean attractors correspond to stable continuous attractors.
  • In more complex networks, non-Boolean switching events influence continuous attractor features.
  • Switching characteristics and pulse propagation explain the continuous-Boolean attractor relationship.

Conclusions:

  • Boolean approximations are effective for simple continuous dynamical systems.
  • Complex logic in networks introduces inherent non-Boolean dynamics that affect attractor stability.
  • Further research is needed to refine Boolean models for complex continuous systems.