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Area of Science:

  • Complex Systems
  • Network Science
  • Nonlinear Dynamics

Background:

  • Oscillatory networks are fundamental in various scientific domains.
  • Network robustness is critical for system functionality, especially when damaged.
  • The aging process, a phase transition, quantifies network resilience by oscillator amplitude vanishing.

Purpose of the Study:

  • To investigate the dynamical robustness of diffusively coupled oscillatory networks with repulsive links.
  • To analytically derive the critical fraction for the aging process in such networks.
  • To understand how repulsive interactions and network damage affect resilience.

Main Methods:

  • Analytical derivation of the critical fraction for the aging process.
  • Numerical verification using coupled Stuart-Landau oscillators.
  • Investigation of network response to varying numbers of repulsive links and symmetry-breaking.

Main Results:

  • Repulsive links enhance the critical threshold, decreasing overall dynamical robustness.
  • A specific percentage of repulsive links can induce an aging process in the entire network.
  • Symmetry-breaking coupling and targeted inactivation further influence network robustness.

Conclusions:

  • Repulsive interactions generally reduce the resilience of coupled oscillatory networks.
  • The aging process serves as a key indicator of network phase transitions and robustness.
  • Findings provide insights into coupling mechanisms and their impact on damaged network dynamics.