Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying Delays
Cellular neural networks with D operator and time-varying delays are found to be effective in demonstrating complex dynamic behaviors. The stability analysis of the pseudo-almost periodic solution for a novel neural network of this kind is considered in this work. A generalized class neural networks...
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| Format: | Article |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1951 |
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| author | Weide Liu Jianliang Huang Qinghe Yao |
| author_facet | Weide Liu Jianliang Huang Qinghe Yao |
| author_sort | Weide Liu |
| collection | DOAJ |
| description | Cellular neural networks with D operator and time-varying delays are found to be effective in demonstrating complex dynamic behaviors. The stability analysis of the pseudo-almost periodic solution for a novel neural network of this kind is considered in this work. A generalized class neural networks model, combining cellular neural networks and the shunting inhibitory neural networks with D operator and time-varying delays is constructed. Based on the fixed-point theory and the exponential dichotomy of linear equations, the existence and uniqueness of pseudo-almost periodic solutions are investigated. Through a suitable variable transformation, the globally exponentially stable sufficient condition of the cellular neural network is examined. Compared with previous studies on the stability of periodic solutions, the global exponential stability analysis for this work avoids constructing the complex Lyapunov functional. Therefore, the stability criteria of the pseudo-almost periodic solution for cellular neural networks in this paper are more precise and less conservative. Finally, an example is presented to illustrate the feasibility and effectiveness of our obtained theoretical results. |
| first_indexed | 2024-03-10T08:37:34Z |
| format | Article |
| id | doaj.art-e4853bc52f7b49afb79fe021929b1d55 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:37:34Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e4853bc52f7b49afb79fe021929b1d552023-11-22T08:34:20ZengMDPI AGMathematics2227-73902021-08-01916195110.3390/math9161951Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying DelaysWeide Liu0Jianliang Huang1Qinghe Yao2School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, ChinaSchool of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, ChinaSchool of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, ChinaCellular neural networks with D operator and time-varying delays are found to be effective in demonstrating complex dynamic behaviors. The stability analysis of the pseudo-almost periodic solution for a novel neural network of this kind is considered in this work. A generalized class neural networks model, combining cellular neural networks and the shunting inhibitory neural networks with D operator and time-varying delays is constructed. Based on the fixed-point theory and the exponential dichotomy of linear equations, the existence and uniqueness of pseudo-almost periodic solutions are investigated. Through a suitable variable transformation, the globally exponentially stable sufficient condition of the cellular neural network is examined. Compared with previous studies on the stability of periodic solutions, the global exponential stability analysis for this work avoids constructing the complex Lyapunov functional. Therefore, the stability criteria of the pseudo-almost periodic solution for cellular neural networks in this paper are more precise and less conservative. Finally, an example is presented to illustrate the feasibility and effectiveness of our obtained theoretical results.https://www.mdpi.com/2227-7390/9/16/1951cellular neural networkspseudo-almost periodic solutionexponential dichotomyD operatortime-varying delays |
| spellingShingle | Weide Liu Jianliang Huang Qinghe Yao Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying Delays Mathematics cellular neural networks pseudo-almost periodic solution exponential dichotomy D operator time-varying delays |
| title | Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying Delays |
| title_full | Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying Delays |
| title_fullStr | Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying Delays |
| title_full_unstemmed | Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying Delays |
| title_short | Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying Delays |
| title_sort | stability analysis of pseudo almost periodic solution for a class of cellular neural network with d operator and time varying delays |
| topic | cellular neural networks pseudo-almost periodic solution exponential dichotomy D operator time-varying delays |
| url | https://www.mdpi.com/2227-7390/9/16/1951 |
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