Frustration and stability in random boolean networks

Abstract Discrete iterations of boolean mappings are known to yield to limit cycles [3, 8]. These limit cycles share a common stable part: the stable core which never oscillate along the different limit cycles. We show that non-frustrated circuits (defined as an extension of [7, 10]) are part of this core. We then characterize non-frustration — thus stability — in terms of the discrete derivative as introduced in [6, 11, 12].