- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Why temporal networks are more controllable: Link weight variation offers superiority

Xin-Ya Zhang1, Jie Sun2, and Gang Yan1,3,4,*

  • 1School of Physical Science and Engineering, Tongji University, Shanghai 200092, People's Republic of China
  • 2Huawei Hong Kong Research Center, Sha Tin, Hong Kong SAR, People's Republic of China
  • 3Shanghai Research Institute of Intelligence Science and Technology, Shanghai 200092, People's Republic of China
  • 4CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, People's Republic of China

  • *Corresponding author: gyan@tongji.edu.cn
PDF

Phys. Rev. Research 3, L032045 – Published 16 August, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032045

Abstract

The control of temporal networks is of paramount importance to complex systems in diverse fields. Recent studies showed that temporal networks are more controllable than their static counterparts, in terms of control time, cost, and trajectory length. However, the underlying mechanism of this intriguing phenomenon remains elusive, partly due to the fact that multiple properties of a temporal network simultaneously change over time. Here, we explore a general model of temporal networks, and prove that the weight variation of a link is equivalent to attaching a virtual driver node to that link. Consequently, the random variation of link weights can significantly increase the dimension of controllable space and remarkably reduce control cost, which unveils the fundamental mechanism for the advantages of temporal networks in controllability. The finding of this mechanism leads to a graphic criterion that allows us to further discover that, degree-heterogeneous networks are more advantageous for enhancing controllability by link weight variation, and the favorable positions of weight variation are the incoming links of the nodes with a high outdegree and a low indegree. Our results are validated in both synthetic and empirical network data, together deepening the understanding of network temporality and shedding light on the long-standing problem of establishing graphic criteria for the controllability of general dynamic systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (43)

  1. P. Holme and J. Saramäki, Temporal networks, Phys. Rep. 519, 97 (2012).
  2. D. S. Bassett, N. F. Wymbs, M. A. Porter, P. J. Mucha, J. M. Carlson, and S. T. Grafton, Dynamic reconfiguration of human brain networks during learning, Proc. Natl. Acad. Sci. USA 108, 7641 (2011).
  3. V. Sekara, A. Stopczynski, and S. Lehmann, Fundamental structures of dynamic social networks, Proc. Natl. Acad. Sci. USA 113, 9977 (2016).
  4. D. Tang, W. Du, L. Shekhtman, Y. Wang, S. Havlin, X. Cao, and G. Yan, Predictability of real temporal networks, Natl. Sci. Rev. 7, 929 (2020).
  5. Y. Ji, W. He, S. Cheng, J. Kurths, and M. Zhan, Dynamic network characteristics of power-electronics-based power systems, Sci. Rep. 10, 9946 (2020).
  6. T. Gross, C. J. D. D'Lima, and B. Blasius, Epidemic Dynamics on an Adaptive Network, Phys. Rev. Lett. 96, 208701 (2006).
  7. N. Masuda, K. Klemm, and V. M. Eguíluz, Temporal Networks: Slowing Down Diffusion by Long Lasting Interactions, Phys. Rev. Lett. 111, 188701 (2013).
  8. I. Scholtes, N. Wider, R. Pfitzner, A. Garas, C. J. Tessone, and F. Schweitzer, Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks, Nat. Commun. 5, 5024 (2014).
  9. E. Valdano, L. Ferreri, C. Poletto, and V. Colizza, Analytical Computation of the Epidemic Threshold on Temporal Networks, Phys. Rev. X 5, 021005 (2015).
  10. M. De Domenico, C. Granell, M. A. Porter, and A. Arenas, The physics of spreading processes in multilayer networks, Nat. Phys. 12, 901 (2016).
  11. O. E. Williams, F. Lillo, and V. Latora, Effects of memory on spreading processes in non-Markovian temporal networks, New J. Phys. 21, 043028 (2019).
  12. A. Koher, H. H. K. Lentz, J. P. Gleeson, and P. Hövel, Contact-Based Model for Epidemic Spreading on Temporal Networks, Phys. Rev. X 9, 031017 (2019).
  13. N. Perra, A. Baronchelli, D. Mocanu, B. Gonçalves, R. Pastor-Satorras, and A. Vespignani, Random Walks and Search in Time-Varying Networks, Phys. Rev. Lett. 109, 238701 (2012).
  14. M. Starnini, A. Baronchelli, A. Barrat, and R. Pastor-Satorras, Random walks on temporal networks, Phys. Rev. E 85, 056115 (2012).
  15. V. Kohar, P. Ji, A. Choudhary, S. Sinha, and J. Kurths, Synchronization in time-varying networks, Phys. Rev. E 90, 022812 (2014).
  16. X. Zhang, S. Boccaletti, S. Guan, and Z. Liu, Explosive Synchronization in Adaptive and Multilayer Networks, Phys. Rev. Lett. 114, 038701 (2015).
  17. D. Levis, I. Pagonabarraga, and A. Díaz-Guilera, Synchronization in Dynamical Networks of Locally Coupled Self-Propelled Oscillators, Phys. Rev. X 7, 011028 (2017).
  18. D. G. Rand, S. Arbesman, and N. A. Christakis, Dynamic social networks promote cooperation in experiments with humans, Proc. Natl. Acad. Sci. USA 108, 19193 (2011).
  19. A. Li, L. Zhou, Q. Su, S. P. Cornelius, Y.-Y. Liu, L. Wang, and S. A. Levin, Evolution of cooperation on temporal networks, Nat. Commun. 11, 2259 (2020).
  20. M. Pósfai and P. Hövel, Structural controllability of temporal networks, New J. Phys. 16, 123055 (2014).
  21. Y. Pan and X. Li, Structural controllability and controlling centrality of temporal networks, PLoS ONE 9, e94998 (2014).
  22. A. Li, S. P. Cornelius, Y.-Y. Liu, L. Wang, and A.-L. Barabási, The fundamental advantages of temporal networks, Science 358, 1042 (2017).
  23. Y. Zhang, A. Garas, and I. Scholtes, Higher-order models capture changes in controllability of temporal networks, J. Phys. Complex. 2, 015007 (2021).
  24. Y.-Y. Liu, J.-J. Slotine, and A.-L. Barabási, Controllability of complex networks, Nature (London) 473, 167 (2011).
  25. T. Nepusz and T. Vicsek, Controlling edge dynamics in complex networks, Nat. Phys. 8, 568 (2012).
  26. G. Yan, J. Ren, Y.-C. Lai, C.-H. Lai, and B. Li, Controlling Complex Networks: How Much Energy is Needed? Phys. Rev. Lett. 108, 218703 (2012).
  27. J. Sun and A. E. Motter, Controllability Transition and Nonlocality in Network Control, Phys. Rev. Lett. 110, 208701 (2013).
  28. S. P. Cornelius, W. L. Kath, and A. E. Motter, Realistic control of network dynamics, Nat. Commun. 4, 1942 (2013).
  29. J. Ruths and D. Ruths, Control profiles of complex networks, Science 343, 1373 (2014).
  30. J. Gao, Y.-Y. Liu, R. M. D'souza, and A.-L. Barabási, Target control of complex networks, Nat. Commun. 5, 5415 (2014).
  31. S. Gu, F. Pasqualetti, M. Cieslak, Q. K. Telesford, A. B. Yu, A. E. Kahn, J. D. Medaglia, J. M. Vettel, M. B. Miller, S. T. Grafton, and D. S. Bassett, Controllability of structural brain networks, Nat. Commun. 6, 8414 (2015).
  32. F. L. Iudice, F. Garofalo, and F. Sorrentino, Structural permeability of complex networks to control signals, Nat. Commun. 6, 8349 (2015).
  33. Y.-Y. Liu and A.-L. Barabási, Control principles of complex systems, Rev. Mod. Phys. 88, 035006 (2016).
  34. I. Klickstein, A. Shirin, and F. Sorrentino, Locally Optimal Control of Complex Networks, Phys. Rev. Lett. 119, 268301 (2017).
  35. G. Menichetti, L. Dall'Asta, and G. Bianconi, Control of multilayer networks, Sci. Rep. 6, 20706 (2016).
  36. X. Liu, L. Pan, H. E. Stanley, and J. Gao, Controllability of giant connected components in a directed network, Phys. Rev. E 95, 042318 (2017).
  37. G. Yan, P. E. Vértes, E. K. Towlson, Y. L. Chew, D. S. Walker, W. R. Schafer, and A.-L. Barabási, Network control principles predict neuron function in the caenorhabditis elegans connectome, Nature (London) 550, 519 (2017).
  38. L. Xiang, F. Chen, W. Ren, and G. Chen, Advances in network controllability, IEEE Circuits Syst. Mag. 19, 8 (2019).
  39. J.-M. Coron, Control and Nonlinearity, Mathematical Surveys and Monographs Vol. 136 (American Mathematical Society, Providence, RI, 2009).
  40. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L032045 for analytical derivation, empirical data, and more numerical results.
  41. K.-I. Goh, B. Kahng, and D. Kim, Universal behavior of load distribution in scale-free networks, Phys. Rev. Lett. 87, 278701 (2001).
  42. T. Nishikawa, J. Sun, and A. E. Motter, Sensitive Dependence of Optimal Network Dynamics on Network Structure, Phys. Rev. X 7, 041044 (2017).
  43. J. D. Hart, Y. Zhang, R. Roy, and A. E. Motter, Topological Control of Synchronization Patterns: Trading Symmetry for Stability, Phys. Rev. Lett. 122, 058301 (2019).

Outline

Information

Phys. Rev. Research 3, L032045– Published 16 August, 2021
  • Received 13 December 2020
  • Revised 23 April 2021
  • Accepted 3 August 2021
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation