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Controllability of multiplex, multi-time-scale networks.

Márton Pósfai1, Jianxi Gao2, Sean P Cornelius2

  • 1Complexity Science Center, University of California, Davis, California 95616, USA; Department of Computer Science, University of California, Davis, California 95616, USA; and Department of Physics of Complex Systems, Eötvös University, Budapest H-1117, Hungary.

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Summary
This summary is machine-generated.

Controlling complex multilayer networks with different time scales is challenging. Applying control to the faster layer enhances controllability, reducing the number of necessary inputs as time-scale differences increase.

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Area of Science:

  • Complex Systems Science
  • Network Theory
  • Control Theory

Background:

  • Layered networks model diverse real-world systems, including biological, social, and transportation networks.
  • Controlling these multilayer systems is challenging due to differing operational time scales, limiting standard control theory applications.

Purpose of the Study:

  • To develop a theory for controlling multilayer, multi-time-scale networks, specifically two-layer multiplex networks.
  • To investigate how applying control signals to one layer affects overall system controllability.

Main Methods:

  • Utilized disjoint path covers to determine the minimum number of control inputs (Nᵢ) required for full network control.
  • Analyzed the impact of time-scale separation between network layers on controllability.

Main Results:

  • When layers share the same time scale, both layers' structures equally influence controllability.
  • Controllability improves when control targets the faster layer, with Nᵢ decreasing as time-scale separation grows.
  • If control targets the slower layer, controllability decreases with increasing time-scale separation, with Nᵢ depending on both layers' structures up to a critical point.

Conclusions:

  • Time-scale separation significantly impacts the controllability of multilayer networks.
  • Targeting the faster layer offers enhanced control, particularly with substantial time-scale differences.
  • Understanding these dynamics is crucial for managing complex interacting systems.