Anomalous Low-Mode Transport and Emergent Medium Behavior in PMIR Rivalry Dynamics

This preprint investigates the response of Phase-Modulated Information Rivalry (PMIR) systems to weak external perturbations applied along controlled spectral directions. PMIR models consist of nonlinear node dynamics coupled through a graph Laplacian, without assuming any underlying continuum geometry, particles, or physical fields.

We introduce an external probe in the form of a small-amplitude step perturbation aligned with the Fiedler eigenmode of the Laplacian and measure the resulting deviation in an ensemble-averaged rivalry observable. Across periodic two-dimensional lattice networks spanning system sizes from N=256N = 256N=256 to N=4096N = 4096N=4096, the probe response exhibits robust power-law scaling in time. The observed scaling exponents are consistently larger than those associated with diffusive or ballistic transport and become increasingly stable as system size increases.

Crucially, the scaling behavior is highly sensitive to probe direction. It appears only when perturbations are aligned with low-frequency global modes and disappears under random or high-frequency excitation. This directional selectivity demonstrates that the response is governed by collective spectral structure rather than by local or stochastic effects.

These results provide evidence for an emergent dynamical medium arising purely from interaction topology and nonlinear dynamics. The medium supports nonlocal, scale-coupled transport without invoking continuum assumptions or geometric embedding. Together with earlier work demonstrating structured rivalry dynamics and spectral convergence, this study positions PMIR as a minimal, testable framework for exploring emergent transport and effective field-like behavior in discrete nonlinear systems.