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Dynamics of self-adjusting systems with noise
Paul Melby1, Nicholas Weber, Alfred Hübler
1Center for Complex Systems Research, Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA. paulmelby@gmail.com
Chaos (Woodbury, N.Y.)
|October 29, 2005
Summary
Noise in self-adjusting systems causes adaptation to the edge of chaos to be a transient phase. Chaotic outbreaks, characterized by a power law distribution, can be triggered by noise.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- Self-adjusting systems exhibit complex dynamics.
- Adaptation to the edge of chaos is a key feature of these systems.
- The role of noise in these dynamics is not fully understood.
Purpose of the Study:
- To investigate the impact of noise on self-adjusting systems.
- To analyze the dynamics of the self-adjusting parameter under noisy conditions.
- To understand the phenomenon of adaptation to the edge of chaos in the presence of noise.
Main Methods:
- Analytical modeling
- Numerical simulations
- Experimental validation
Main Results:
- System dynamics can be described by a rescaled diffusion equation.
- Adaptation to the edge of chaos is a transient effect when noise is present.
- Noise induces chaotic outbreaks with power-law distributed lengths.
Conclusions:
- Noise significantly alters the dynamics of self-adjusting systems.
- The edge of chaos is a transient state, not a stable attractor, in noisy systems.
- Chaotic outbreaks are a notable consequence of noise, exhibiting predictable statistical properties.