Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument
In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the cont...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/9/1754 |
| _version_ | 1797482055481688064 |
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| author | Marat Akhmet Madina Tleubergenova Roza Seilova Zakhira Nugayeva |
| author_facet | Marat Akhmet Madina Tleubergenova Roza Seilova Zakhira Nugayeva |
| author_sort | Marat Akhmet |
| collection | DOAJ |
| description | In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introduced approach of recurrent motions checking, is effectively utilized. The existence and asymptotic properties of the unique Poisson stable motion are investigated. Simulation examples for results are provided. Finally, comparing impulsive shunting inhibitory cellular neural networks with former neural network models, we discuss the significance of the components of our model. |
| first_indexed | 2024-03-09T22:22:50Z |
| format | Article |
| id | doaj.art-1e45adde6baa4fdd87ec7c164d1d75ea |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:22:50Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-1e45adde6baa4fdd87ec7c164d1d75ea2023-11-23T19:10:25ZengMDPI AGSymmetry2073-89942022-08-01149175410.3390/sym14091754Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant ArgumentMarat Akhmet0Madina Tleubergenova1Roza Seilova2Zakhira Nugayeva3Department of Mathematics, Middle East Technical University, 06800 Ankara, TurkeyDepartment of Mathematics, Aktobe Regional University, Aktobe 030000, KazakhstanDepartment of Mathematics, Aktobe Regional University, Aktobe 030000, KazakhstanDepartment of Mathematics, Aktobe Regional University, Aktobe 030000, KazakhstanIn the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introduced approach of recurrent motions checking, is effectively utilized. The existence and asymptotic properties of the unique Poisson stable motion are investigated. Simulation examples for results are provided. Finally, comparing impulsive shunting inhibitory cellular neural networks with former neural network models, we discuss the significance of the components of our model.https://www.mdpi.com/2073-8994/14/9/1754impulsive shunting inhibitory cellular neural networkssymmetry of impulsive and differential partscontinuous and impact activationsgeneralized piecewise constant argumentmethod of included intervalscontinuous and discontinuous Poisson stable inputs and outputs |
| spellingShingle | Marat Akhmet Madina Tleubergenova Roza Seilova Zakhira Nugayeva Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument Symmetry impulsive shunting inhibitory cellular neural networks symmetry of impulsive and differential parts continuous and impact activations generalized piecewise constant argument method of included intervals continuous and discontinuous Poisson stable inputs and outputs |
| title | Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument |
| title_full | Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument |
| title_fullStr | Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument |
| title_full_unstemmed | Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument |
| title_short | Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument |
| title_sort | poisson stability in symmetrical impulsive shunting inhibitory cellular neural networks with generalized piecewise constant argument |
| topic | impulsive shunting inhibitory cellular neural networks symmetry of impulsive and differential parts continuous and impact activations generalized piecewise constant argument method of included intervals continuous and discontinuous Poisson stable inputs and outputs |
| url | https://www.mdpi.com/2073-8994/14/9/1754 |
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