Principal spectral theory and variational characterizations for nonlocal coupled cooperative systems and applications

[2607.20288] Principal spectral theory and variational characterizations for nonlocal coupled cooperative systems and applications Skip to main content Search Submit Donate Log in Mathematics > Analysis of PDEs arXiv:2607.20288 (math) [Submitted on 22 Jul 2026 ( v1 ), last revised 22 Aug 2026 (this version, v2)] Title: Principal spectral theory and variational characterizations for nonlocal coupled cooperative systems and applications Authors: Xiandong Lin , Jiazhuo Cheng , Qiru Wang View PDF HTML (experimental) Abstract: This paper investigates the principal spectral theory of a nonlocal dispersal operator with coupled diffusion and aims to establish a variational characterization of the spectral bound for the case where the system is not strongly coupled. In this setting, a key difficulty arises since the principal eigenfunction may have components that are identically zero, rendering existing generalized eigenvalue methods inapplicable. To overcome this, we reorder the components of the operator using a permutation matrix, thereby decomposing it into suitable suboperators, and characterize the spectral bound of the original operator in terms of the spectral bounds of these suboperators. Building on this principal spectral theory, we provide a variational characterization of the basic reproduction ratio for nonlocal dispersal systems and analyze the dynamical behavior of a class of multi-genotype stem cell regeneration models with epigenetic transitions, both in the presence and absence of gene mutations, without assuming the existence of a principal eigenvalue. Furthermore, we investigate the threshold dynamics when the system is not strongly coupled. Comments: 30 pages, 3 figures Subjects: Analysis of PDEs (math.AP) MSC classes: 45C05, 35K57, 35R20, 92D25 Cite as: arXiv:2607.20288 [math.AP] (or arXiv:2607.20288v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2607.20288 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Qi-Ru Wang [ view email ] [v1] Wed, 22 Jul 2026 15:36:06 UTC (5,610 KB) [v2] Sat, 22 Aug 2026 10:54:29 UTC (5,611 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2026-07 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• Principal spectral theory and variational characterizations for nonlocal coupled cooperative systems and applications#665866
• A new perspective on the equivalence between Weak and Strong Spatial Mixing in two dimensions#160853
• Geometric Fluctuations of the $\sinΘ$ Distance in High-Dimensional Principal Subspace Estimation#984651
• Statistical levels and spatial modes of Fock-space heterogeneity in many-body localization crossovers#1109352
• On spatial decoherence in many-body systems#986533