| Boolean models are often used to obtain insights into the dynamics of physical systems composed of elements that appear to execute binary logic. The attractor structure of a Boolean network depends strongly on the scheme chosen for updating the nodes. In an autonomous Boolean network (ABN), time delays are assigned to the links and each node is updated continuously according to the values of its inputs at the appropriate previous times. I will describe how generic features of physical systems can be incorporated into ABNs and show the dramatic effects they have on the attractor structure of two simple systems: rings of one-input nodes; and a single XOR gate with two self-inputs. Related effects in large, complex networks will also be presented. Finally, I will briefly describe recent efforts to construct an ABN model of the gene regulatory network governing early embryonic development in the sea urchin. |
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