Additional repulsion reduces the dynamical resilience in the damaged networks

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.