Abstract
We introduce the discrete automaton models of gene networks with weight functions of vertices accounting for the various forms of the regulatory interaction of agents. We study the discrete mapping that describes the operation of a fragment of the gene network of the bacteria E. coli. For this mapping, we find its fixed points (stationary states) on using the SAT approach. We also study the mappings that are defined by the random graphs of the network which we generate in accordance with the Gilbert-Erdos-Renyi and Watts-Strogatz models. For these mappings, we find the fixed points and the length 2 and 3 cycles. This article can be regarded as a survey of our results on the discrete models of gene networks and the numerical methods for studying their operation.
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