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Updated: Jun 24, 2025
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Synchronization transitions in phase oscillator populations with partial adaptive coupling.
Zhenyu Chen1, Zhigang Zheng2, Can Xu2
1School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China.
Chaos (Woodbury, N.Y.)
|June 3, 2024
Summary
This study reveals how adaptation in coupled oscillators influences synchronization. Nonzero adaptation drives explosive or continuous transitions, depending on system correlations, offering new control mechanisms for networked systems.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Adaptation is crucial for collective dynamics in many systems.
- Synchronization transitions are fundamental to networked systems.
- Understanding adaptive mechanisms is key to controlling system behavior.
Purpose of the Study:
- To investigate the conditions for synchronization transitions in adaptive coupled phase oscillators.
- To analyze the role of feedback between coupling and order parameter.
- To explore how adaptation influences the nature of phase transitions.
Main Methods:
- Mathematical analysis of coupled phase oscillators with adaptive feedback.
- Investigation of power-law functions relating coupling and order parameter.
- Examination of subcritical and supercritical correlation scenarios.
Main Results:
- No critical adaptive fraction is needed for first- to second-order or vice-versa transitions.
- Nonzero adaptation leads to explosive or continuous phase transitions.
- Synchronization routes depend on relative adaptive weights and scaling behaviors near criticality.
Conclusions:
- Adaptation significantly alters synchronization transitions in coupled oscillator systems.
- The findings provide insights into the dynamical nature of phase transitions.
- This work aids in controlling and manipulating synchronization in adaptive networks.
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