4.8 Article

Optimal resilience of modular interacting networks

出版社

NATL ACAD SCIENCES
DOI: 10.1073/pnas.1922831118

关键词

interacting network; resilience; percolation; optimal phenomenon

资金

  1. National Natural Science Foundation of China [71690242, 61973143, 71974080, 11731014]
  2. National Key R&D Program of China [2020YFA0608601]
  3. Young backbone teachers of Jiangsu Province
  4. Natural Science Foundation of China [61773248, 71771152, 72032003, 71632006]
  5. Major Program of the National Fund of Philosophy and Social Science of China [20ZDA060, 18ZDA088]
  6. NSF [PHY-1505000, CMMI-1125290]
  7. Bar-Ilan Presidential Scholarship program
  8. Israel Science Foundation
  9. Binational Science Foundation
  10. National Science Foundation, Defense Threat Reduction Agency
  11. Israel Science Foundation-National Science Foundation of China joint program

向作者/读者索取更多资源

The research indicates that in modular networks, an optimal fraction of interconnected nodes exists where the system becomes optimally resilient and is able to withstand more damage. Although the exact location of the optimal fraction varies based on the coupling patterns, there exists such an optimal point for all coupling patterns.
Coupling between networks is widely prevalent in real systems and has dramatic effects on their resilience and functional properties. However, current theoretical models tend to assume homogeneous coupling where all the various subcomponents interact with one another, whereas real-world systems tend to have various different coupling patterns. We develop two frameworks to explore the resilience of such modular networks, including specific deterministic coupling patterns and coupling patterns where specific subnetworks are connected randomly. We find both analytically and numerically that the location of the percolation phase transition varies nonmonotonically with the fraction of interconnected nodes when the total number of interconnecting links remains fixed. Furthermore, there exists an optimal fraction r* of interconnected nodes where the system becomes optimally resilient and is able to withstand more damage. Our results suggest that, although the exact location of the optimal r* varies based on the coupling patterns, for all coupling patterns, there exists such an optimal point. Our findings provide a deeper understanding of network resilience and show how networks can be optimized based on their specific coupling patterns.

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