## 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.