A winding pump phase in a ring of parametric oscillators creates a single unidirectional, topologically protected phase dislocation whose speed can be tuned and stopped by pump amplitude.
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In every dimension d≥2 there exists a unique β_*^{(d)}>0 such that the uniform density on the sphere is the unique global minimizer of the USA free energy up to the linear-stability threshold K_# for β≤β_*, yielding a continuous transition, while for β>β_* the uniform density is not globally minimiz
Defines temporal matrix scale invariance (tMSI) for correlation kernels, decouples dynamical exponent α from spectral exponent β via Mellin factorization, and classifies tipping points by the sign of an exact Landau quartic coefficient a4 derived from those exponents and a three-point structure cons
A self-consistent framework with generalized local order parameters is derived for the Kuramoto model with dyadic and triadic interactions on hypergraphs, showing bistability onset depends on eigenvector correlations between dyadic and triadic structures.
Introduces graph-to-image prediction of per-node dynamic stability landscapes in oscillator networks from topology, releases two 10k-graph datasets, and shows GNN-CNN models achieve good accuracy with cross-size generalization.
Mixed-sign feedback disorder in Kuramoto-coupled active rotator networks reshapes pinning-drift balance, with weak coupling suppressing drift and stronger coupling restoring it when disorder is moderate.
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A winding pump phase in a ring of parametric oscillators creates a single unidirectional, topologically protected phase dislocation whose speed can be tuned and stopped by pump amplitude.
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Phase transitions for the noisy transformer model in arbitrary dimension
In every dimension d≥2 there exists a unique β_*^{(d)}>0 such that the uniform density on the sphere is the unique global minimizer of the USA free energy up to the linear-stability threshold K_# for β≤β_*, yielding a continuous transition, while for β>β_* the uniform density is not globally minimiz
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Temporal Matrix Scale Invariance and the Classification of Tipping Points
Defines temporal matrix scale invariance (tMSI) for correlation kernels, decouples dynamical exponent α from spectral exponent β via Mellin factorization, and classifies tipping points by the sign of an exact Landau quartic coefficient a4 derived from those exponents and a three-point structure cons
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Self-consistent analysis of the Kuramoto model with higher-order interactions
A self-consistent framework with generalized local order parameters is derived for the Kuramoto model with dyadic and triadic interactions on hypergraphs, showing bistability onset depends on eigenvector correlations between dyadic and triadic structures.
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Learning Dynamic Stability Landscapes in Synchronization Networks
Introduces graph-to-image prediction of per-node dynamic stability landscapes in oscillator networks from topology, releases two 10k-graph datasets, and shows GNN-CNN models achieve good accuracy with cross-size generalization.
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Collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback disorder
Mixed-sign feedback disorder in Kuramoto-coupled active rotator networks reshapes pinning-drift balance, with weak coupling suppressing drift and stronger coupling restoring it when disorder is moderate.