Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delays
Abstract This paper considers the Clifford-valued recurrent neural network (RNN) models, as an augmentation of real-valued, complex-valued, and quaternion-valued neural network models, and investigates their global exponential stability in the Lagrange sense. In order to address the issue of non-com...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-05-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03415-8 |
| _version_ | 1818597679533391872 |
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| author | G. Rajchakit R. Sriraman N. Boonsatit P. Hammachukiattikul C. P. Lim P. Agarwal |
| author_facet | G. Rajchakit R. Sriraman N. Boonsatit P. Hammachukiattikul C. P. Lim P. Agarwal |
| author_sort | G. Rajchakit |
| collection | DOAJ |
| description | Abstract This paper considers the Clifford-valued recurrent neural network (RNN) models, as an augmentation of real-valued, complex-valued, and quaternion-valued neural network models, and investigates their global exponential stability in the Lagrange sense. In order to address the issue of non-commutative multiplication with respect to Clifford numbers, we divide the original n-dimensional Clifford-valued RNN model into 2 m n $2^{m}n$ real-valued models. On the basis of Lyapunov stability theory and some analytical techniques, several sufficient conditions are obtained for the considered Clifford-valued RNN models to achieve global exponential stability according to the Lagrange sense. Two examples are presented to illustrate the applicability of the main results, along with a discussion on the implications. |
| first_indexed | 2024-12-16T11:51:38Z |
| format | Article |
| id | doaj.art-4e12609704b54f67bf137262dffbdc86 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-16T11:51:38Z |
| publishDate | 2021-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4e12609704b54f67bf137262dffbdc862022-12-21T22:32:41ZengSpringerOpenAdvances in Difference Equations1687-18472021-05-012021112110.1186/s13662-021-03415-8Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delaysG. Rajchakit0R. Sriraman1N. Boonsatit2P. Hammachukiattikul3C. P. Lim4P. Agarwal5Department of Mathematics, Faculty of Science, Maejo UniversityDepartment of Mathematics, Thiruvalluvar UniversityDepartment of Mathematics, Rajamangala University of Technology SuvarnabhumiDepartment of Mathematics, Phuket Rajabhat UniversityInstitute for Intelligent Systems Research and Innovation, Deakin UniversityDepartment of Mathematics, Anand International College of EngineeringAbstract This paper considers the Clifford-valued recurrent neural network (RNN) models, as an augmentation of real-valued, complex-valued, and quaternion-valued neural network models, and investigates their global exponential stability in the Lagrange sense. In order to address the issue of non-commutative multiplication with respect to Clifford numbers, we divide the original n-dimensional Clifford-valued RNN model into 2 m n $2^{m}n$ real-valued models. On the basis of Lyapunov stability theory and some analytical techniques, several sufficient conditions are obtained for the considered Clifford-valued RNN models to achieve global exponential stability according to the Lagrange sense. Two examples are presented to illustrate the applicability of the main results, along with a discussion on the implications.https://doi.org/10.1186/s13662-021-03415-8Clifford-valued neural networkExponential stabilityLyapunov functionalLagrange stability |
| spellingShingle | G. Rajchakit R. Sriraman N. Boonsatit P. Hammachukiattikul C. P. Lim P. Agarwal Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delays Advances in Difference Equations Clifford-valued neural network Exponential stability Lyapunov functional Lagrange stability |
| title | Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delays |
| title_full | Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delays |
| title_fullStr | Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delays |
| title_full_unstemmed | Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delays |
| title_short | Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delays |
| title_sort | exponential stability in the lagrange sense for clifford valued recurrent neural networks with time delays |
| topic | Clifford-valued neural network Exponential stability Lyapunov functional Lagrange stability |
| url | https://doi.org/10.1186/s13662-021-03415-8 |
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