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Advances in the Mathematical Theory of WPAA Dynamics for Impulsive High Order Neural Systems in Clifford Algebras
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GAMA Laboratory (LR21ES10), Department of Mathematics, Faculty of Sciences of Bizerte, University of Carthage, Bizerte 7021, Tunisia
* Corresponding Author:
Chaouki Aouiti,
[email protected]
Volume 2, Issue 1
2026
Received: 23 October 2025
Accepted: 09 January 2026
Published: 21 January 2026
Article Information
Published in
Journal of Nonlinear Dynamics and Applications
Volume/Issue
Volume 2, Issue 1, 2026
Pages
1-12
Cited by
1 (Crossref)
Abstract
The primary objective of this work is to establish the existence, uniqueness, and exponential stability of piecewise weighted pseudo–almost automorphic solutions for impulsive high-order Hopfield neural networks formulated within Clifford algebras. Using the Banach fixed-point principle together with a suitably adapted Gronwall–Bellman inequality, we derive novel and verifiable sufficient conditions that ensure these qualitative properties. The main contributions are as follows: (i) this study is the first to analyze weighted pseudo–almost automorphic (WPAA) dynamics for impulsive high-order Hopfield neural networks directly in the Clifford algebra setting, without reducing the model to real-valued components; (ii) it offers a unified framework that accommodates both first- and second-order synaptic interactions under impulsive perturbations and mixed delays; and (iii) the resulting conditions explicitly capture the geometric structure of Clifford-valued states, providing a broader and algebraically consistent formulation compared to real or quaternion-valued models. The theoretical findings are further supported by a numerical example demonstrating their applicability and effectiveness.
Graphical Abstract
Keywords
impulsive systems
WPAA-functions
HOHNNs
Gronwall–Bellman inequality
exponential stability
clifford algebra
Data Availability Statement
No datasets were generated or analyzed during the current study.
Funding
This work was supported without any funding.
Conflicts of Interest
The authors declare no conflicts of interest.
AI Use Statement
The authors declare that no generative AI was used in the preparation of this manuscript.
Ethical Approval and Consent to Participate
Not applicable.
References
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Cited By (1)
-
Chaouki Aouiti, Mahjouba Ben Rezek. Pseudo S-asymptotically $$\omega $$-antiperiodic behavior in delayed Cohen–Grossberg neural networks.
Journal of Elliptic and Parabolic Equations, 2026 .
[CrossRef]
* Citation data provided by Crossref Cited-by.
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APA Style
Aouiti, C.& Dridi, F. (2025). Advances in the Mathematical Theory of WPAA Dynamics for Impulsive High Order Neural Systems in Clifford Algebras. Journal of Nonlinear Dynamics and Applications, 2(1), 1–12. https://doi.org/10.62762/JNDA.2025.838385
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TY - JOUR AU - Aouiti, Chaouki AU - Dridi, Farah PY - 2026 DA - 2026/01/21 TI - Advances in the Mathematical Theory of WPAA Dynamics for Impulsive High Order Neural Systems in Clifford Algebras JO - Journal of Nonlinear Dynamics and Applications T2 - Journal of Nonlinear Dynamics and Applications JF - Journal of Nonlinear Dynamics and Applications VL - 2 IS - 1 SP - 1 EP - 12 DO - 10.62762/JNDA.2025.838385 UR - https://www.icck.org/article/abs/JNDA.2025.838385 KW - impulsive systems KW - WPAA-functions KW - HOHNNs KW - Gronwall–Bellman inequality KW - exponential stability KW - clifford algebra AB - The primary objective of this work is to establish the existence, uniqueness, and exponential stability of piecewise weighted pseudo–almost automorphic solutions for impulsive high-order Hopfield neural networks formulated within Clifford algebras. Using the Banach fixed-point principle together with a suitably adapted Gronwall–Bellman inequality, we derive novel and verifiable sufficient conditions that ensure these qualitative properties. The main contributions are as follows: (i) this study is the first to analyze weighted pseudo–almost automorphic (WPAA) dynamics for impulsive high-order Hopfield neural networks directly in the Clifford algebra setting, without reducing the model to real-valued components; (ii) it offers a unified framework that accommodates both first- and second-order synaptic interactions under impulsive perturbations and mixed delays; and (iii) the resulting conditions explicitly capture the geometric structure of Clifford-valued states, providing a broader and algebraically consistent formulation compared to real or quaternion-valued models. The theoretical findings are further supported by a numerical example demonstrating their applicability and effectiveness. SN - 3069-6313 PB - Institute of Central Computation and Knowledge LA - English ER -
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@article{Aouiti2026Advances,
author = {Chaouki Aouiti and Farah Dridi},
title = {Advances in the Mathematical Theory of WPAA Dynamics for Impulsive High Order Neural Systems in Clifford Algebras},
journal = {Journal of Nonlinear Dynamics and Applications},
year = {2026},
volume = {2},
number = {1},
pages = {1-12},
doi = {10.62762/JNDA.2025.838385},
url = {https://www.icck.org/article/abs/JNDA.2025.838385},
abstract = {The primary objective of this work is to establish the existence, uniqueness, and exponential stability of piecewise weighted pseudo–almost automorphic solutions for impulsive high-order Hopfield neural networks formulated within Clifford algebras. Using the Banach fixed-point principle together with a suitably adapted Gronwall–Bellman inequality, we derive novel and verifiable sufficient conditions that ensure these qualitative properties. The main contributions are as follows: (i) this study is the first to analyze weighted pseudo–almost automorphic (WPAA) dynamics for impulsive high-order Hopfield neural networks directly in the Clifford algebra setting, without reducing the model to real-valued components; (ii) it offers a unified framework that accommodates both first- and second-order synaptic interactions under impulsive perturbations and mixed delays; and (iii) the resulting conditions explicitly capture the geometric structure of Clifford-valued states, providing a broader and algebraically consistent formulation compared to real or quaternion-valued models. The theoretical findings are further supported by a numerical example demonstrating their applicability and effectiveness.},
keywords = {impulsive systems, WPAA-functions, HOHNNs, Gronwall–Bellman inequality, exponential stability, clifford algebra},
issn = {3069-6313},
publisher = {Institute of Central Computation and Knowledge}
}
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