The dynamics of directed NOR networks

Jeremiah Rogers

This work investigates the dynamics of simultaneously updated boolean networks defined on directed graphs, where each vertex updates to the logical NOR value of the states of the vertices in its in-neighborhood. We prove the existence and number of limit cycles and the width of state space graphs for directed cycles, complete graphs, and complete bipartite graphs. We show that every strongly connected graph has a limit cycle of length 2, and that steady states correspond to independent sets of vertices which dominate all of the graph but themselves.