Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument
A new model of inertial neural networks with a generalized piecewise constant argument as well as unpredictable inputs is proposed. The model is inspired by unpredictable perturbations, which allow to study the distribution of chaotic signals in neural networks. The existence and exponential stabili...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/4/620 |
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| author | Marat Akhmet Madina Tleubergenova Zakhira Nugayeva |
| author_facet | Marat Akhmet Madina Tleubergenova Zakhira Nugayeva |
| author_sort | Marat Akhmet |
| collection | DOAJ |
| description | A new model of inertial neural networks with a generalized piecewise constant argument as well as unpredictable inputs is proposed. The model is inspired by unpredictable perturbations, which allow to study the distribution of chaotic signals in neural networks. The existence and exponential stability of unique unpredictable and Poisson stable motions of the neural networks are proved. Due to the generalized piecewise constant argument, solutions are continuous functions with discontinuous derivatives, and, accordingly, Poisson stability and unpredictability are studied by considering the characteristics of continuity intervals. That is, the piecewise constant argument requires a specific component, the Poisson triple. The <i>B</i>-topology is used for the analysis of Poisson stability for the discontinuous functions. The results are demonstrated by examples and simulations. |
| first_indexed | 2024-03-11T05:03:32Z |
| format | Article |
| id | doaj.art-db639aa77a88491388881efdb7d1497a |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T05:03:32Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-db639aa77a88491388881efdb7d1497a2023-11-17T19:08:39ZengMDPI AGEntropy1099-43002023-04-0125462010.3390/e25040620Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant ArgumentMarat Akhmet0Madina Tleubergenova1Zakhira Nugayeva2Department of Mathematics, Middle East Technical University, Ankara 06800, TurkeyDepartment of Mathematics, Aktobe Regional University, Aktobe 030000, KazakhstanDepartment of Mathematics, Aktobe Regional University, Aktobe 030000, KazakhstanA new model of inertial neural networks with a generalized piecewise constant argument as well as unpredictable inputs is proposed. The model is inspired by unpredictable perturbations, which allow to study the distribution of chaotic signals in neural networks. The existence and exponential stability of unique unpredictable and Poisson stable motions of the neural networks are proved. Due to the generalized piecewise constant argument, solutions are continuous functions with discontinuous derivatives, and, accordingly, Poisson stability and unpredictability are studied by considering the characteristics of continuity intervals. That is, the piecewise constant argument requires a specific component, the Poisson triple. The <i>B</i>-topology is used for the analysis of Poisson stability for the discontinuous functions. The results are demonstrated by examples and simulations.https://www.mdpi.com/1099-4300/25/4/620inertial neural networksgeneralized piecewise constant argumentunpredictable oscillationsPoisson stable oscillationsunpredictable input–outputsPoisson triple |
| spellingShingle | Marat Akhmet Madina Tleubergenova Zakhira Nugayeva Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument Entropy inertial neural networks generalized piecewise constant argument unpredictable oscillations Poisson stable oscillations unpredictable input–outputs Poisson triple |
| title | Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument |
| title_full | Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument |
| title_fullStr | Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument |
| title_full_unstemmed | Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument |
| title_short | Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument |
| title_sort | unpredictable and poisson stable oscillations of inertial neural networks with generalized piecewise constant argument |
| topic | inertial neural networks generalized piecewise constant argument unpredictable oscillations Poisson stable oscillations unpredictable input–outputs Poisson triple |
| url | https://www.mdpi.com/1099-4300/25/4/620 |
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