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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]
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Database: Engineering Source
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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]
ISSN:09252312
DOI:10.1016/j.neucom.2026.133787