Research The Long-range Correlation Of Random Boolean Networks

Various systems,such as physical, social and biological, generate complex fluctuations with correlations across multiple time scales.One kind of fluctuation situated between"white noise"possessing small time scales criterion rough and great time criterion smooth and"Brownian noise"possessing small time criterion smooth and great time criterion rough, we name it as the 1 f low frequency power spectrum decay. It which occupies partial randomness, has the relevant critical state macroscopically. This kind of noise changes rhythms tally with person's pats organism signal under peaceful condition and cycle of brainαwave. The relevance of these signals which change result from disease and caducity, will deviate the 1 ffluctuation. Although this kind of related tendency is very important in the actual production and the basic research, the reason produced still is unknown. To seek this reason of fluctuation, we must first establish model which can produce this kind of fluctuation . The Boolean network that is most basic and important method, can actually portray the genetic network systematically. It describes the gene regulation network multiple structure as a powerful tool. Simultaneously, also carries on the network system dynamics analysis effectively.Dynamic characteristic of the network usually is divided into: Order, critical and disorder. The ordered nature in fact corresponds stably, but the disorder reflects the sensitivity of the system to outside stimulation. Located nearby phase transition area, system between the order and the chaos usually is called the critical system. The massive researches demonstrated: The cellular network, specially the gene regulation network, possibly is the movement between the order and the disorder critical state. The Boolean network sensitivity, 0 < S <1, S =1and S >1 ,corresponds system's order, critical and the chaos state separately. In the article, We use the critical state of Boolean network to simulate physiology system for studying its dynamic behavior. we mainly study three factors on influence of the stochastic Boolean network dynamic behavior: Boolean function sensitivity, connection between Boolean network nodes, size of stochastic increase noise in Boolean network evolutionary process.We discovered: (1) when k_e=3and k_e=4the stochastic Boolean network may produce 1 f. (2)When noise is low, the output of the networks is similar to the Brown noise, as the noise increased, the output of the networks gradually transforminto the 1 f region, and ultimately close to the white noise.This is quite consistent with the living system to ambient noise's response. To that extent, the controllable noise scope to study the network dynamic behavior is quite of importance. (3) With Boolean function sensitivity value's increase, the whole long distance relevant value of the network displace downward, which is quite consistent with our initial forecast's influence of Boolean function to the Boolean network dynamic behavior. (4) The network produces the fluctuation 1 fregion to be bigger k_e=3 than k_e=4.