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arXiv · 2606.15852

Structural Oscillatority Criterion of Boolean Networks

Hiroki Kodama
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Abstract

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

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Hiroki Kodama. 2026-07-30. Structural Oscillatority Criterion of Boolean Networks. https://arxiv.org/abs/2606.15852

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