Coherence Percolation and Morphological Transitions in Density-Regulated Phase Networks

This work investigates the emergence of large-scale coherent structures in a two-dimensional network of phase oscillators regulated by local stress feedback and density transport. Using numerical simulations, we show that coherence organization is governed by morphological transitions rather than global synchronization alone. We identify fragmented, percolating, and critical regimes, and demonstrate the existence of a robust operating point characterized by reproducible dominance of a coherent domain. Morphological observables such as domain size distributions and dominance ratios are shown to provide essential insight beyond scalar order parameters.