Numerical and Theoretical Studies of Noise Effects in the Kauffman Model

Details Numerical and Theoretical Studies of Noise Effects in the Kauffman Model Numerical and Theoretical Studies of Noise Effects in the Kauffman Model

2002-07-09

arxiv.org/abs/nlin/0207016v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

24 pages, 9 figures, Submitted to the Journal of Statistical Physics

Scientific paper

In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a similar kind of behavior, even when the structure of their basins of attraction is quite different. This can be considered as a robust property of these models. We present numerical results for the full range of noise level and obtain approximate analytic expressions for the above crossing time as a function of the noise in the limit cases of small and large noise levels.

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