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Stepanov-like pseudo almost automorphic dynamics of stochastic inertial shunting inhibitory cellular neural networks.

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Title: Stepanov-like pseudo almost automorphic dynamics of stochastic inertial shunting inhibitory cellular neural networks.
Authors: Zhou, Yisen1 (AUTHOR), Li, Yongkun1 (AUTHOR) yklie@ynu.edu.cn
Source: Neurocomputing. Jul2026, Vol. 687, pN.PAG-N.PAG. 1p.
Subjects: Cellular neural networks (Computer science), Stochastic differential equations, Mathematics, Stability theory, Time delay systems, Fixed point theory, Artificial neural networks
Abstract: This paper focuses on the dynamics of stochastic shunting inhibitory cellular neural networks with time delays. While significant research has been devoted to almost automorphic solutions for deterministic neural networks, the study of Stepanov-like pseudo almost automorphy in distribution for stochastic systems remains largely unexplored. To address a foundational gap, this work first introduces a novel and rigorous definition for Stepanov-like pseudo almost automorphic stochastic processes in distribution, overcoming limitations of existing moment-based characterizations. Under this new framework, we establish pioneering results on the existence and stability of such solutions for a class of stochastic delayed shunting inhibitory cellular neural networks, employing the Banach fixed point theorem and inequality techniques. The theoretical findings are validated through a concrete numerical example. This work not only provides the first systematic analysis of Stepanov-like pseudo almost automorphic solutions in distribution for stochastic neural networks but also offers a methodological framework applicable to other stochastic differential equations. [ABSTRACT FROM AUTHOR]
Copyright of Neurocomputing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 193722542
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Stepanov-like pseudo almost automorphic dynamics of stochastic inertial shunting inhibitory cellular neural networks.
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  Data: <searchLink fieldCode="AR" term="%22Zhou%2C+Yisen%22">Zhou, Yisen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Yongkun%22">Li, Yongkun</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yklie@ynu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Neurocomputing%22">Neurocomputing</searchLink>. Jul2026, Vol. 687, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Cellular+neural+networks+%28Computer+science%29%22">Cellular neural networks (Computer science)</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+differential+equations%22">Stochastic differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Time+delay+systems%22">Time delay systems</searchLink><br /><searchLink fieldCode="DE" term="%22Fixed+point+theory%22">Fixed point theory</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink>
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  Label: Abstract
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  Data: This paper focuses on the dynamics of stochastic shunting inhibitory cellular neural networks with time delays. While significant research has been devoted to almost automorphic solutions for deterministic neural networks, the study of Stepanov-like pseudo almost automorphy in distribution for stochastic systems remains largely unexplored. To address a foundational gap, this work first introduces a novel and rigorous definition for Stepanov-like pseudo almost automorphic stochastic processes in distribution, overcoming limitations of existing moment-based characterizations. Under this new framework, we establish pioneering results on the existence and stability of such solutions for a class of stochastic delayed shunting inhibitory cellular neural networks, employing the Banach fixed point theorem and inequality techniques. The theoretical findings are validated through a concrete numerical example. This work not only provides the first systematic analysis of Stepanov-like pseudo almost automorphic solutions in distribution for stochastic neural networks but also offers a methodological framework applicable to other stochastic differential equations. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Neurocomputing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.neucom.2026.133787
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Cellular neural networks (Computer science)
        Type: general
      – SubjectFull: Stochastic differential equations
        Type: general
      – SubjectFull: Mathematics
        Type: general
      – SubjectFull: Stability theory
        Type: general
      – SubjectFull: Time delay systems
        Type: general
      – SubjectFull: Fixed point theory
        Type: general
      – SubjectFull: Artificial neural networks
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      – TitleFull: Stepanov-like pseudo almost automorphic dynamics of stochastic inertial shunting inhibitory cellular neural networks.
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            NameFull: Li, Yongkun
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              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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