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Tiered synchronization in Kuramoto oscillators with adaptive higher-order interactions
Priyanka Rajwani1, Ayushi Suman1, Sarika Jalan1
1Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India.
Adaptation in higher-order interactions restores second-order phase transitions and introduces tiered synchronization. This finding is crucial for understanding complex natural systems with feedback coupling.
Area of Science:
- Complex systems dynamics
- Nonlinear dynamics and chaos theory
Background:
- Phase transitions are common in natural systems.
- Higher-order interactions can shift phase transitions from second-order to first-order synchronization.
- Existing models often focus on pairwise interactions.
Purpose of the Study:
- To investigate the effect of adaptation in higher-order interactions on phase transitions.
- To explore the emergence of novel synchronization phenomena.
- To provide a theoretical framework for understanding complex system dynamics.
Main Methods:
- Analysis of coupled dynamics incorporating higher-order interactions and adaptation.
- Utilizing the Ott-Antonsen manifold to describe system states.
- Identifying bifurcations and phase transition behaviors.
Main Results:
- Adaptation in higher-order interactions restores the second-order phase transition.
- A novel phenomenon termed 'tiered synchronization' emerges.
- Tiered synchronization results from a combination of super-critical pitchfork and two saddle node bifurcations.
Conclusions:
- Higher-order interactions and adaptation play a critical role in phase transitions.
- The Ott-Antonsen manifold effectively describes tiered synchronization and system stability.
- Findings are vital for modeling real-world systems with feedback coupling and inherent higher-order interactions.
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