Abstract
In the study of complex networks, simple local heterogeneous interactions favor highly complicated and non-linear dynamics. In this paper, we take advantage of recent advances presented by Rosas et al [Physical Review E, 100, 032305] to capture the fundamentals of dynamics: high-order interdependencies. In particular, the phase diagram of Random Boolean Networks is described in terms of the information shared between multiple nodes. We found that the critical point between ordered and chaotic regimes is well defined by a balance between redundancy and synergy, for both normal and scale-free topologies. In addition, particular network structures are identified that characterize the behavior of high-order interdependencies in each dynamic regime.
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Notes
- 1.
It should be noted that this result is of a statistical nature, since it is possible to find chaotic networks in the predicted stable regime and vice versa.
- 2.
Being in fact the only structure capable of achieving this, since the union set of attractors corresponds precisely to two fixed points with maximum Hamming distance.
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Orellana, S., Moreira, A. (2021). Multivariate Information in Random Boolean Networks. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications IX. COMPLEX NETWORKS 2020 2020. Studies in Computational Intelligence, vol 943. Springer, Cham. https://doi.org/10.1007/978-3-030-65347-7_49
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