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Published (Version of record)CC BY V4.0, Open Access
Journal article
Scale free topology as an effective feedback system
PLoS Computational Biology, Vol.16(5), 1007825
11/May/2020
Abstract
Biological networks are often heterogeneous in their connectivity pattern, with degree distributions featuring a heavy tail of highly connected hubs. The implications of this heterogeneity on dynamical properties are a topic of much interest. Here we show that interpreting topology as a feedback circuit can provide novel insights on dynamics. Based on the observation that in finite networks a small number of hubs have a disproportionate effect on the entire system, we construct an approximation by lumping these nodes into a single effective hub, which acts as a feedback loop with the rest of the nodes. We use this approximation to study dynamics of networks with scale-free degree distributions, focusing on their probability of convergence to fixed points. We find that the approximation preserves convergence statistics over a wide range of settings. Our mapping provides a parametrization of scale free topology which is predictive at the ensemble level and also retains properties of individual realizations. Specifically, outgoing hubs have an organizing role that can drive the network to convergence, in analogy to suppression of chaos by an external drive. In contrast, incoming hubs have no such property, resulting in a marked difference between the behavior of networks with outgoing vs. incoming scale free degree distribution. Combining feedback analysis with mean field theory predicts a transition between convergent and divergent dynamics which is corroborated by numerical simulations. Furthermore, they highlight the effect of a handful of outlying hubs, rather than of the connectivity distribution law as a whole, on network dynamics.
Details
- Title
- Scale free topology as an effective feedback system
- Creators
- Alexander Rivkind (null) - Technion – Israel Institute of Technology (Israel, Haifa)Hallel Schreier (null) - Technion – Israel Institute of Technology (Israel, Haifa)Naama Brenner (Corresponding Author) - Technion – Israel Institute of Technology (Israel, Haifa)Omri Barak (null) - Technion – Israel Institute of Technology (Israel, Haifa)
- Resource Type
- Journal article
- Publication Details
- PLoS Computational Biology, Vol.16(5), 1007825; 11/May/2020
- Number of pages
- 24
- Language
- English
- DOI
- https://doi.org/10.1371/journal.pcbi.1007825
- Grant note
- This work was supported in part by the Israeli Science Foundation (isf.org.il grant number 346/16, OB; and grant number 155/18, NB). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
- Record Identifier
- 993265504503596
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