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Synchronization in adaptive higher-order networks.
Md Sayeed Anwar1,2, S Nirmala Jenifer3, Paulsamy Muruganandam3
1Indian Statistical Institute, Physics and Applied Mathematics Unit, 203 B. T. Road, Kolkata 700108, India.
Physical Review. E
|February 7, 2025
Summary
This study introduces adaptive higher-order networks to model complex systems with group interactions. It reveals conditions for stable synchronization, showing how group dynamics and adaptation influence system behavior.
Area of Science:
- Complex Systems Science
- Network Science
- Nonlinear Dynamics
Background:
- Complex systems often exhibit group interactions that change over time.
- Existing adaptive network models primarily focus on pairwise interactions, neglecting group dynamics.
Purpose of the Study:
- To develop a general framework for adaptive higher-order networks that incorporates both adaptivity and group interactions.
- To identify the conditions necessary for stable global synchronization in such systems.
Main Methods:
- Proposed a general framework for adaptive higher-order networks.
- Analyzed systems with adaptive pairwise interactions and then extended to adaptive higher-order interactions.
- Utilized the master stability equation to derive conditions for synchronization.
Main Results:
- Demonstrated the existence of global synchronization in adaptive higher-order networks.
- Identified necessary conditions for stable synchronous states, separating dynamical and structural properties.
- Showcased findings using coupled generalized Kuramoto oscillators with phase lag.
Conclusions:
- The interplay of group interactions and adaptive connectivity creates stability regions, enabling transitions between synchronization and desynchronization.
- Higher-order adaptation significantly impacts synchronization stability compared to constant higher-order interactions.
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