Aging in global networks with competing attractive-Repulsive interaction.
Shiva Dixit1, Paul Asir M1, Manish Dev Shrimali1
1Department of Physics, Central University of Rajasthan, NH-8, Bandar Sindri, Ajmer 305 817, India.
Chaos (Woodbury, N.Y.)
|December 31, 2020
Summary
We investigated networks of coupled oscillators with both attractive and repulsive interactions. A critical fraction of repulsive nodes induces network inactivity, resembling an aging transition.
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.
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