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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.21058 |
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Table of Contents:
- Chimera states, characterized by the coexistence of coherent and incoherent domains, represent a paradigm of self-organization in complex systems. In this study, we introduce a topological analysis method based on winding numbers to characterize the dynamics of spiral wave chimeras in a two-dimensional phase oscillator network. Our investigation reveals distinct scaling laws governing the system's evolution across the phase lag $α$. Perturbation analysis in the limit $α\to 0$ demonstrates that the incoherent core radius scales linearly with $α$. In contrast, within the stable chimera regime, the average total positive winding number $μ$ follows a clear exponential growth law $μ= ae^{bα}$. This scaling disparity signals a physical crossover from a regime dominated by geometric core expansion to one driven by active topological excitation. Furthermore, we identify a statistical transition in the defect distribution from binomial-like to Poisson-like behavior at a critical threshold $α^*$. These results demonstrate that topological defects possess intrinsic statistical order, establishing $μ$ as a robust macro-variable for analyzing the structural complexity of chimera states.