Complex Systems

Stability of Equilibrial States and Limit Cycles in Sparsely Connected, Structurally Complex Boolean Nets Download PDF

Crayton C. Walker
Department of Information Management, University of Connecticut,
368 Fairfield Road, Storrs, CT 06268, USA


Through their natural dynamics, networks of Boolean functions can recompute, or return to, equilibrial states and limit cycles from which they have been displaced. How often such return occurs measures one kind of behavioral stability. For a class of functionally homogeneous, sparsely connected, disorderly structured networks, this paper examines how stability of equilibrial states and limit cycles is affected by the size of the net, size of the displacement, and the function used in the net. All functions in the class are examined, and displacement is varied over its full range. On the whole, for any given function, the effect of displacement size appears to be quite regular. However, from function to function, displacement effects vary widely. Though there are exceptions, at a given relative displacement, most functions show decreasing cyclic stability as nets become larger. On the other hand, the data suggest that for many functions, larger nets are more stable under small absolute displacements.