Principal profiles, characteristic communication and critical asymptotics for cooperative nonlocal systems on the circle
Abstract
We study cooperative nonlocal transport on a circle with species-dependent constant velocities and arbitrary L1 probability kernels. For periodic coefficients, the period map is a compact perturbation of the no-jump map. We construct separate receiving and sending characteristic scans: under a two-tree condition based at one active component, a positive Floquet profile exists exactly when the full period map has strictly larger spectral radius than its no-jump part. The other jump rates may vanish. The scans provide an integral minorant and positive jump return; a separate coefficient inequality verifies the spectral gap. Smooth locking examples distinguish communication from frozen-time mixing, while a resonant example separates positive return from spectral separation. Autonomous nonzero velocities and union-graph connectivity yield a simple principal pair; one active component suffices for exponential mixing. We also prove local perturbation results. For quadratic self-regulation, the same principal projection gives a transverse response whose averaged cubic coefficient is a nonnegative asymptotic variance. It determines both the critical t−2log t correction and the second-order period-averaged amplitude of the positive branch.
Related
- Singular analysis of the principal eigenvalue for cooperative elliptic systems with drifts
- Regularity Effects on the Small-Diffusion Asymptotics of the Principal Eigenvalue: Non-convergence and Convergence
- Generalized Transition Fronts and Spectral Speed Asymptotics in Heterogeneous Cooperative Systems
- Asymptotics for number of indecomposable components of tensor powers of the natural SL2-module in odd characteristic
- Cooperative Multi-Task Semantic Communication for Joint Classification and Regression Tasks
BibTeX
@misc{he2026principal,
title = {{Principal profiles, characteristic communication and critical asymptotics for cooperative nonlocal systems on the circle}},
author = {Bing He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36851},
eprint = {2610.36851},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36851},
}
RIS
TY - UNPB
TI - Principal profiles, characteristic communication and critical asymptotics for cooperative nonlocal systems on the circle
AU - Bing He
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36851
UR - https://arxiv.org/abs/2610.36851
AB - We study cooperative nonlocal transport on a circle with species-dependent constant velocities and arbitrary L^1 probability kernels. For periodic coefficients, the period map is a compact perturbation of the no-jump map. We construct separate receiving and sending characteristic scans: under a two-tree condition based at one active component, a positive Floquet profile exists exactly when the full period map has strictly larger spectral radius than its no-jump part. The other jump rates may vanish. The scans provide an integral minorant and positive jump return; a separate coefficient inequality verifies the spectral gap. Smooth locking examples distinguish communication from frozen-time mixing, while a resonant example separates positive return from spectral separation. Autonomous nonzero velocities and union-graph connectivity yield a simple principal pair; one active component suffices for exponential mixing. We also prove local perturbation results. For quadratic self-regulation, the same principal projection gives a transverse response whose averaged cubic coefficient is a nonnegative asymptotic variance. It determines both the critical t^−2log t correction and the second-order period-averaged amplitude of the positive branch.
ER -