Barrier heights in the Kauffman model

We consider two versions of the Kauffman model (the quenched and the annealed models) in presence of thermal noise. When we compare the time evolution of two configurations subjected to the same thermal noise, we find for both versions of the Kauffman model that below a critical temperature T c , the time τ 2 for these two configurations to become identical increases exponentially with the system size N. This defines a barrier height which can be calculated analytically for the annealed model only. When we compare more than two configurations, we observe that the time τ n it takes for at least two configurations among n to meet increases also exponentially. The slope of log τ n versus the system size N seems to be the same for all n and for both models Nous considerons deux versions du modele de Kauffman (le modele gele et le modele recuit) en presence de bruit. Quand on compare deux configurations soumises au meme bruit thermique, on observe que, pour ces deux versions du modele de Kauffman, au-dessous d'une temperature critique T c , le temps τ 2 qu'il faut pour que les deux configurations se rejoignent augmente exponentiellement avec la taille N du systeme. Cela definit une hauteur de barriere qui peut etre calculee analytiquement pour le modele recuit. Quand on compare plus que deux configurations, on observe que les temps τ n pour qu'au moins deux configurations parmi n se rencontrent augmentent aussi exponentiellement. La pente de log τ n en fonction de N semble etre la meme pour tout n et pour les deux modeles

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