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Controllability of higher-order networks

Author

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  • Ma, Weiyuan
  • Bao, Xionggai
  • Ma, Chenjun

Abstract

Higher-order networks can comprehensively describe interactions among groups, thus emerging as a novel area of exploration in network science. This paper aims to delve into the controllability of higher-order networks, where the network topology is characterized by higher-order interactions and the nodes are higher-dimensional dynamical systems. The collective effects on the network controllability from the dynamics of higher-order interactions, node dynamics, inner interactions, and external control inputs are extensively explored. By applying matrix theory and control theory, some necessary and/or sufficient conditions are developed to determine the controllability of hypergraph networks and simplicial complex networks. Through simulated examples, it becomes evident that the controllability of higher-order networked system is far more complicated than that of traditional networked systems and the higher-order topological structures facilitate the controllability. Remarkably, the integrated network can achieve controllability even when the corresponding traditional network is uncontrollable by external inputs.

Suggested Citation

  • Ma, Weiyuan & Bao, Xionggai & Ma, Chenjun, 2024. "Controllability of higher-order networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 653(C).
    • Handle: RePEc:eee:phsmap:v:653:y:2024:i:c:s0378437124006174
    DOI: 10.1016/j.physa.2024.130108
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    References listed on IDEAS

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