Structural Oscillatority Criterion of Boolean Networks

Abstract

Azuma et al. showed that a cactus-expandable Boolean network $\hat{I}\pounds$ is structurally oscillatory if all the simple cycles of $\hat{I}\pounds$ contain an odd number of inhibiting edges. We show that we do not need the cactus-expandable condition. Namely, a strongly connected Boolean network $\hat{I}\pounds$ is structurally oscillatory if and only if all the simple cycles of $\hat{I}\pounds$ contain an odd number of inhibiting edges. Additionally, we provide a characterization of a structurally oscillatory Boolean network for the general case.

11 pages, 4 figures, 1 table