New proof on exponential convergence for cellular neural networks with time-varying delays
Abstract In this paper, we deal with a class of cellular neural networks with time-varying delays. Applying differential inequality strategies without assuming the boundedness conditions on the activation functions, we obtain a new sufficient condition that ensures that all solutions of the consider...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-07-01
|
| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1235-8 |
| _version_ | 1819087918456635392 |
|---|---|
| author | Changjin Xu Peiluan Li |
| author_facet | Changjin Xu Peiluan Li |
| author_sort | Changjin Xu |
| collection | DOAJ |
| description | Abstract In this paper, we deal with a class of cellular neural networks with time-varying delays. Applying differential inequality strategies without assuming the boundedness conditions on the activation functions, we obtain a new sufficient condition that ensures that all solutions of the considered neural networks converge exponentially to the zero equilibrium point. We give an example to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies of Tang (Appl. Math. Lett. 21:872–876, 2008). |
| first_indexed | 2024-12-21T21:43:47Z |
| format | Article |
| id | doaj.art-43121eeebee14e56b3a8c1a4fc127c1c |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-21T21:43:47Z |
| publishDate | 2019-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-43121eeebee14e56b3a8c1a4fc127c1c2022-12-21T18:49:18ZengSpringerOpenBoundary Value Problems1687-27702019-07-012019111010.1186/s13661-019-1235-8New proof on exponential convergence for cellular neural networks with time-varying delaysChangjin Xu0Peiluan Li1Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and EconomicsSchool of Mathematics and Statistics, Henan University of Science and TechnologyAbstract In this paper, we deal with a class of cellular neural networks with time-varying delays. Applying differential inequality strategies without assuming the boundedness conditions on the activation functions, we obtain a new sufficient condition that ensures that all solutions of the considered neural networks converge exponentially to the zero equilibrium point. We give an example to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies of Tang (Appl. Math. Lett. 21:872–876, 2008).http://link.springer.com/article/10.1186/s13661-019-1235-8Cellular neural networksExponential convergenceTime-varying delayTime-varying coefficients |
| spellingShingle | Changjin Xu Peiluan Li New proof on exponential convergence for cellular neural networks with time-varying delays Boundary Value Problems Cellular neural networks Exponential convergence Time-varying delay Time-varying coefficients |
| title | New proof on exponential convergence for cellular neural networks with time-varying delays |
| title_full | New proof on exponential convergence for cellular neural networks with time-varying delays |
| title_fullStr | New proof on exponential convergence for cellular neural networks with time-varying delays |
| title_full_unstemmed | New proof on exponential convergence for cellular neural networks with time-varying delays |
| title_short | New proof on exponential convergence for cellular neural networks with time-varying delays |
| title_sort | new proof on exponential convergence for cellular neural networks with time varying delays |
| topic | Cellular neural networks Exponential convergence Time-varying delay Time-varying coefficients |
| url | http://link.springer.com/article/10.1186/s13661-019-1235-8 |
| work_keys_str_mv | AT changjinxu newproofonexponentialconvergenceforcellularneuralnetworkswithtimevaryingdelays AT peiluanli newproofonexponentialconvergenceforcellularneuralnetworkswithtimevaryingdelays |