Topological defects in spiral wave chimera states

Abstract

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 $\alpha$. Perturbation analysis in the limit $\alpha \to 0$ demonstrates that the incoherent core radius scales linearly with $\alpha$. In contrast, within the stable chimera regime, the average total positive winding number $\mu$ follows a clear exponential growth law $\mu = ae^{b\alpha}$. 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 $\alpha^*$. These results demonstrate that topological defects possess intrinsic statistical order, establishing $\mu$ as a robust macro-variable for analyzing the structural complexity of chimera states.