Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant Arguments
There are three principal novelties in the present investigation. It is the first time Cohen–Grossberg-type neural networks are considered with the most general delay and advanced piecewise constant arguments. The model is alpha unpredictable in the sense of electrical inputs and is researched under...
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MDPI AG
2025-03-01
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| Series: | Mathematics |
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| author | Marat Akhmet Zakhira Nugayeva Roza Seilova |
| author_facet | Marat Akhmet Zakhira Nugayeva Roza Seilova |
| author_sort | Marat Akhmet |
| collection | DOAJ |
| description | There are three principal novelties in the present investigation. It is the first time Cohen–Grossberg-type neural networks are considered with the most general delay and advanced piecewise constant arguments. The model is alpha unpredictable in the sense of electrical inputs and is researched under the conditions of alpha unpredictable and Poisson stable outputs. Thus, the phenomenon of ultra Poincaré chaos, which can be indicated through the analysis of a single motion, is now confirmed for a most sophisticated neural network. Moreover, finally, the approach of pseudo-quasilinear reduction, in its most effective form is now expanded for strong nonlinearities with time switching. The complexity of the discussed model makes it universal and useful for various specific cases. Appropriate examples with simulations that support the theoretical results are provided. |
| format | Article |
| id | doaj-art-cfee5fe313324814ae6a77f01b1963ae |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-cfee5fe313324814ae6a77f01b1963ae2025-08-20T02:09:11ZengMDPI AGMathematics2227-73902025-03-01137106810.3390/math13071068Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant ArgumentsMarat Akhmet0Zakhira Nugayeva1Roza Seilova2Department of Mathematics, Middle East Technical University, Ankara 06800, TurkeyDepartment of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, KazakhstanDepartment of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, KazakhstanThere are three principal novelties in the present investigation. It is the first time Cohen–Grossberg-type neural networks are considered with the most general delay and advanced piecewise constant arguments. The model is alpha unpredictable in the sense of electrical inputs and is researched under the conditions of alpha unpredictable and Poisson stable outputs. Thus, the phenomenon of ultra Poincaré chaos, which can be indicated through the analysis of a single motion, is now confirmed for a most sophisticated neural network. Moreover, finally, the approach of pseudo-quasilinear reduction, in its most effective form is now expanded for strong nonlinearities with time switching. The complexity of the discussed model makes it universal and useful for various specific cases. Appropriate examples with simulations that support the theoretical results are provided.https://www.mdpi.com/2227-7390/13/7/1068Cohen–Grossberg type neural networksalpha unpredictable neural networksPoisson stable piecewise constant argumentmethod of pseudo-quasilinear reductionmethod of included intervalsultra Poincare chaos |
| spellingShingle | Marat Akhmet Zakhira Nugayeva Roza Seilova Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant Arguments Mathematics Cohen–Grossberg type neural networks alpha unpredictable neural networks Poisson stable piecewise constant argument method of pseudo-quasilinear reduction method of included intervals ultra Poincare chaos |
| title | Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant Arguments |
| title_full | Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant Arguments |
| title_fullStr | Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant Arguments |
| title_full_unstemmed | Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant Arguments |
| title_short | Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant Arguments |
| title_sort | alpha unpredictable cohen grossberg neural networks with poisson stable piecewise constant arguments |
| topic | Cohen–Grossberg type neural networks alpha unpredictable neural networks Poisson stable piecewise constant argument method of pseudo-quasilinear reduction method of included intervals ultra Poincare chaos |
| url | https://www.mdpi.com/2227-7390/13/7/1068 |
| work_keys_str_mv | AT maratakhmet alphaunpredictablecohengrossbergneuralnetworkswithpoissonstablepiecewiseconstantarguments AT zakhiranugayeva alphaunpredictablecohengrossbergneuralnetworkswithpoissonstablepiecewiseconstantarguments AT rozaseilova alphaunpredictablecohengrossbergneuralnetworkswithpoissonstablepiecewiseconstantarguments |