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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Coupled oscillator networks are fundamental to understanding emergent phenomena.
  • Investigating the interplay of attractive and repulsive forces is crucial for complex system dynamics.

Purpose of the Study:

  • To analyze the dynamical inactivity in globally coupled identical oscillators with mixed interactions.
  • To determine the critical fraction of repulsive nodes leading to network steady states.
  • To explore symmetry breaking and emergent states like chimera and mixed states.

Main Methods:

  • Analytical derivation of the relationship between coupling strength and critical fraction (p_c).
  • Numerical simulations to corroborate analytical findings.
  • Analysis of diverse oscillator dynamics including limit cycle, chaos, and bursting behaviors.

Main Results:

  • A critical fraction of repulsive nodes (p_c) induces macroscopic network inactivity.
  • The network's inactivity follows an aging transition due to competing interactions.
  • Asymmetry in interactions leads to symmetry breaking, resulting in chimera-like and mixed states.
  • Results are consistent across sequential and random selection of repulsive nodes.

Conclusions:

  • The competition between attractive and repulsive coupling dictates network macroscopic inactivity.
  • Emergent phenomena like aging transitions and chimera states are controllable via interaction parameters.
  • The findings are robust across different dynamical regimes of the constituent oscillators.