Topological defects in spiral wave chimera states

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Network Science

Background:

• Chimera states exhibit coexisting coherent and incoherent domains, a key example of self-organization.
• Understanding the dynamics and structural complexity of chimera states is crucial for complex systems research.

Purpose of the Study:

• To introduce and apply a novel topological analysis method using winding numbers to characterize spiral wave chimeras.
• To investigate the influence of phase lag (α) on chimera state dynamics and identify distinct scaling laws.
• To establish a robust macrovariable for analyzing the structural complexity of chimera states.

Main Methods:

• Topological analysis utilizing winding numbers.
• Perturbation analysis in the limit α→0.
• Statistical analysis of defect distribution.

Main Results:

• Identified distinct scaling laws for chimera state evolution across phase lag α.
• Demonstrated linear scaling of incoherent core radius with α for α→0.
• Revealed exponential growth of average total positive winding number (μ=ae^{bα}) in the stable chimera regime.
• Observed a statistical transition in defect distribution from binomial-like to Poisson-like at a critical threshold α*.

Conclusions:

• The scaling disparity indicates a crossover from geometric core expansion to topological excitation-driven dynamics.
• Topological defects exhibit intrinsic statistical order, with μ serving as a robust macrovariable.
• The developed method provides new insights into the structural complexity and dynamics of chimera states.