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Dynamics of asynchronous random Boolean networks with asynchrony generated by stochastic processes.

Xutao Deng1, Huimin Geng, Mihaela Teodora Matache

  • 1Department of Computer Science, University of Nebraska at Omaha, Omaha, NE 68182-0243, USA.

Bio Systems
|July 28, 2006
PubMed
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This study explores asynchronous Boolean networks using various stochastic processes to control node updates. The number of updated nodes significantly influences system dynamics, promoting order or chaos.

Area of Science:

  • Complex Systems
  • Computational Biology
  • Statistical Physics

Background:

  • Asynchronous Boolean networks (ABNs) are models of complex systems where node states update asynchronously.
  • Previous models used random distributions for asynchrony, focusing on constant or variable parent nodes.
  • Stochastic processes offer a more nuanced approach to generating asynchronous updates.

Purpose of the Study:

  • To investigate the dynamics of ABNs using novel stochastic processes for node update generation.
  • To analyze the impact of the number of updated nodes on system behavior, including sensitivity, bifurcation, and fixed points.
  • To compare the effects of different stochastic processes (Poisson, random walk, birth-death, Brownian motion, fractional Brownian motion) on network dynamics.

Main Methods:

Related Experiment Videos

  • Utilized existing ABN models with constant and variable parent nodes.
  • Introduced stochastic processes (Poisson, random walk, birth-death, Brownian motion, fractional Brownian motion) to control the number of nodes updated per time step.
  • Analyzed system dynamics through sensitivity to initial values, bifurcation diagrams, and fixed-point analysis.

Main Results:

  • The number of updated nodes is crucial, particularly for random walk, birth-death, and Brownian motion processes.
  • Small to moderate numbers of updated nodes generally lead to ordered dynamics.
  • Large numbers of updated nodes can induce chaotic behavior, contingent on underlying parameters.
  • The Poisson process consistently promotes order.
  • Fractional Brownian motion shows increased order with higher Hurst parameter values.

Conclusions:

  • The choice of stochastic process and the number of updated nodes significantly shape the emergent behavior of asynchronous Boolean networks.
  • Order-to-chaos transitions are controllable through parameter selection in these stochastic ABNs.
  • This research provides insights into designing and understanding complex dynamical systems through controlled asynchrony.