Abstract
Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. Thus, even if the system is at equilibrium in a normal functional state, there might exist also a potential stable state having abnormal activity, into which the system might transition due to an external perturbation. Such a system can be regarded as unsustainable, due to the danger of falling into the potential undesired abnormal state. Here we explore, analytically and via simulations, how supporting the activity of a small fraction of nodes can turn an unsustainable system to become sustainable by eliminating the undesired potential stable state. We unveil a sustaining phase diagram in the presence of a fraction of controlled nodes. This phase diagram could provide how many controlled nodes are required for sustaining a given network as well as how strong the connectivity of the network should be for a given fraction of controllable nodes.
| Original language | English |
|---|---|
| Article number | 22 |
| Journal | Communications Physics |
| Volume | 6 |
| Issue number | 1 |
| DOIs | |
| State | Published - Dec 2023 |
Bibliographical note
Funding Information:H.S. acknowledges the support of the Presidential Fellowship of Bar-Ilan University, Israel, and the Mordecai and Monique Katz Graduate Fellowship Program. We thank the Israel Science Foundation, the Binational Israel-China Science Foundation (Grant No. 3132/19), the NSF-BSF (Grant No. 2019740), the EU H2020 project RISE (Project No. 821115), the EU H2020 DIT4TRAM, and DTRA (Grant No. HDTRA-1-19-1-0016) for financial support.
Publisher Copyright:
© 2023, The Author(s).