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Synchronization of Kuromoto Oscillators on Simplicial Complexes: Hysteresis, Cluster Formation and Partial
1Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400088, India.
Entropy (Basel, Switzerland)
|March 28, 2025
Summary
Analyzing oscillator synchronization on simplicial complexes reveals diverse patterns. Factors like network structure and higher-order interactions influence abrupt or smooth transitions and cluster synchronization, relevant to nanomaterials and brain connectomes.
Area of Science:
- Complex systems
- Network science
- Nonlinear dynamics
Background:
- Oscillator synchronization is fundamental in various scientific fields.
- Simplicial complexes offer a framework to study complex network structures beyond pairwise interactions.
- Understanding synchronization dynamics is crucial for applications in physics, biology, and engineering.
Purpose of the Study:
- To analyze the synchronization phenomena in oscillator systems built upon simplicial complexes.
- To investigate how network topology, interaction types, and initial conditions affect synchronization.
- To explore the role of higher-order interactions and geometric features in synchronization patterns.
Main Methods:
- Mathematical modeling of coupled oscillators on simplicial complex networks.
- Analysis of synchronization transitions (abrupt vs. smooth) based on system parameters.
- Quantification of synchronization using order parameters for partial and complete synchronization.
- Investigation of cluster synchronization in different network architectures (sparse, mixed, compact).
- Identification of key factors like frustration and topological effects influencing synchronization.
Main Results:
- Synchronization transitions can be abrupt or smooth, influenced by substrate, frequency, and phase distributions.
- Partial and complete synchronization are observable and quantifiable.
- Higher-order interactions, especially those with opposing signs, significantly alter synchronization dynamics.
- Cluster synchronization emerges on sparse lattices, dependent on spectral dimension and network type.
- Topological effects and the geometry of shared faces are critical determinants of synchronization patterns.
- Frustration is identified as a key factor driving observed synchronization effects.
Conclusions:
- Simplicial complexes provide a rich framework for studying complex synchronization behaviors.
- Network structure, interaction complexity, and geometric properties profoundly impact oscillator synchronization.
- The findings have implications for understanding emergent phenomena in systems like nanomaterials and brain connectomes.
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