Andrew Wuensche

Paper #: 02-02-004

The state space of a discrete dynamical network is connected into basins of attraction, mathematical objects that can be computed and shown as graphs for small networks. Multiple attractors explain how the same genetic regulatory network can maintain different stable patterns of gene activation, the cell types in multicellular organisms. Ideas of modularity suggest that the overall genetic network is actually made up of semi-independent subnetworks. Each subnetwork also settles into one of a range of attractors according to its current state, which if perturbed can cause the dynamics to jump to alternative attractors. A network's "memory," its ability to categorize, is provided by its separate basins of attraction, and also by the topology of the trees and subtrees rooted on each attractor.