| _version_ | 1866901748583497728 |
|---|---|
| author | SCHORR, RICHARD |
| author_facet | SCHORR, RICHARD |
| contents | <p>We study how network topology influences frequency–dependent rivalry dynamics in coupled linear oscillator systems, under progressively stronger structural controls. Using degree-matched and Laplacian spectrum-matched null models, we isolate which topological features materially affect rivalry measures beyond trivial degree effects.</p> <p>Networks with fixed mean degree are generated across three canonical families: ring lattices, small-world graphs, and random regular graphs. For each realization, we simulate a linear diffusive network driven at two nearby frequencies and quantify rivalry using phase-locking–based response asymmetry across a controlled frequency detuning grid. We define summary metrics including mean absolute rivalry, collapse depth, and detuning of maximal response.</p> <p>To separate structural mechanisms, we compare real graphs against (i) degree-sequence–preserving nulls and (ii) spectrum-matched nulls constructed via degree-preserving edge swaps optimized to reproduce the lowest non-zero Laplacian eigenvalues. We further measure spectral indicators, including algebraic connectivity and Fiedler vector localization and overlap at driven nodes.</p> <p>Results show that degree matching alone does not remove topology-dependent rivalry effects, while partial spectral matching substantially reduces them in random regular graphs. In contrast, lattice and small-world topologies resist accurate low-eigenvalue spectral matching under degree constraints, indicating that higher-order spectral structure and eigenvector geometry play a functional role. Correlations between rivalry strength, algebraic connectivity, and Fiedler mode localization support this interpretation.</p> <p>These findings demonstrate that rivalry dynamics are sensitive not merely to degree statistics or global spectral density, but to specific low-mode Laplacian structure. The framework establishes a controlled experimental path for linking network topology, spectral geometry, and dynamical competition, providing a foundation for future extensions to nonlinear dynamics and field-theoretic interpretations.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18210474 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Topology-Dependent Rivalry Dynamics in Degree- and Spectrum-Controlled Networks SCHORR, RICHARD <p>We study how network topology influences frequency–dependent rivalry dynamics in coupled linear oscillator systems, under progressively stronger structural controls. Using degree-matched and Laplacian spectrum-matched null models, we isolate which topological features materially affect rivalry measures beyond trivial degree effects.</p> <p>Networks with fixed mean degree are generated across three canonical families: ring lattices, small-world graphs, and random regular graphs. For each realization, we simulate a linear diffusive network driven at two nearby frequencies and quantify rivalry using phase-locking–based response asymmetry across a controlled frequency detuning grid. We define summary metrics including mean absolute rivalry, collapse depth, and detuning of maximal response.</p> <p>To separate structural mechanisms, we compare real graphs against (i) degree-sequence–preserving nulls and (ii) spectrum-matched nulls constructed via degree-preserving edge swaps optimized to reproduce the lowest non-zero Laplacian eigenvalues. We further measure spectral indicators, including algebraic connectivity and Fiedler vector localization and overlap at driven nodes.</p> <p>Results show that degree matching alone does not remove topology-dependent rivalry effects, while partial spectral matching substantially reduces them in random regular graphs. In contrast, lattice and small-world topologies resist accurate low-eigenvalue spectral matching under degree constraints, indicating that higher-order spectral structure and eigenvector geometry play a functional role. Correlations between rivalry strength, algebraic connectivity, and Fiedler mode localization support this interpretation.</p> <p>These findings demonstrate that rivalry dynamics are sensitive not merely to degree statistics or global spectral density, but to specific low-mode Laplacian structure. The framework establishes a controlled experimental path for linking network topology, spectral geometry, and dynamical competition, providing a foundation for future extensions to nonlinear dynamics and field-theoretic interpretations.</p> |
| title | Topology-Dependent Rivalry Dynamics in Degree- and Spectrum-Controlled Networks |
| url | https://doi.org/10.5281/zenodo.18210474 |