{
  "abstract": "This paper generalizes stochastic sampled-data synchronization of reaction–diffusion neural networks (RDNNs) from sampling distributions with finite support to infinite discrete distributions, whose sampling intervals are drawn from a countably infinite set {qi}i=1∞ with probabilities {αi}i=1∞. Four regularity conditions are identified—finite interval mean, summability of the weighted absolute decay parameters, strict positivity of the probability-averaged decay rate, and boundedness above of the decay parameters, which makes the Lyapunov–Krasovskii functional (LKF) mode-independent in its delay weight and hence continuous across sampling instants. A mode-dependent LKF is constructed, the weak-law step is replaced by the strong law of large numbers combined with a Cesàro-type argument, and the infinite family of design linear matrix inequalities (LMIs) is handled by a truncation-with-tail-verification procedure, for which a rigorous certificate is given: when the tail decay parameters are non-positive, the tail conditions are affine and are certified by corner-point feasibility checks with shared variables; otherwise, a convergent-tail argument applies. Almost-sure exponential synchronization with an explicit rate is established, which implies synchronization in probability, and controller design conditions are derived in terms of LMIs; three examples (two neural networks and one reaction–diffusion neural network) corroborate the design through computed gains, verified tail conditions, stochastic closed-loop simulations, an N-sensitivity analysis, and a comparison with a fixed-period controller. The proposed framework removes the finite-support restriction on the sampling distribution and yields an almost-sure, rate-explicit synchronization guarantee with a numerically verifiable LMI design.",
  "abstract_shown": true,
  "affiliations": [
    "Key Laboratory of Numerical Simulation of Sichuan Provincial Universities, School of Mathematics and Big Data, Neijiang Normal University, Neijiang 641100, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Deqiang Zeng",
      "orcid": "0000-0001-6885-9696"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8qe2wbv5qwf4v.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203665",
  "fulltext_url": null,
  "id": "8qe2wbv5qwf4v",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3665",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1705|Neural Networks Stability and Synchronization"
    ]
  ],
  "openalex": "W7221318504",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/8qe2wbv5qwf4v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203665",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3665"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Synchronization in Probability of Reaction–Diffusion Neural Networks Under Stochastic Sampling Governed by Infinite Discrete Distributions",
  "title_text": "Synchronization in Probability of Reaction–Diffusion Neural Networks Under Stochastic Sampling Governed by Infinite Discrete Distributions",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/8qe2wbv5qwf4v",
  "venue": "Mathematics",
  "versions": []
}