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Dynamical Behavior And Influence Of Stochastic Noise On Certain Generalized Boolean Networks, Gary L. Beck, Mihaela Teodora Matache
Dynamical Behavior And Influence Of Stochastic Noise On Certain Generalized Boolean Networks, Gary L. Beck, Mihaela Teodora Matache
Mathematics Faculty Publications
This study considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number of parent nodes. The network is analyzed when the connectivity k is fixed or variable. Making use of a Boolean rule that is a generalization of Rule 22 of elementary cellular automata, a generalized formula for providing the probability of finding a node in state 1 at a time t is determined. We show typical behaviors of the iterations, and we study the dynamics of the network through Lyapunov exponents, bifurcation diagrams, and fixed point analysis. We conclude …