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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
Summary
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:
- 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.
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