### Abstract

Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.

Original language | English |
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Article number | 028301 |

Journal | Physical review letters |

Volume | 119 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jul 14 2017 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Physical review letters*,

*119*(2), [028301]. https://doi.org/10.1103/PhysRevLett.119.028301