On the Global Practical Exponential Stability of <i>h</i>-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying Delays
In this paper, we focus on <i>h</i>-manifolds related to impulsive reaction–diffusion Cohen–Grossberg neural networks with time-varying delays. By constructing a new Lyapunov-type function and a comparison principle, sufficient conditions that guarantee the global practical exponential s...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/2/188 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850082332044689408 |
|---|---|
| author | Gani Stamov Trayan Stamov Ivanka Stamova Cvetelina Spirova |
| author_facet | Gani Stamov Trayan Stamov Ivanka Stamova Cvetelina Spirova |
| author_sort | Gani Stamov |
| collection | DOAJ |
| description | In this paper, we focus on <i>h</i>-manifolds related to impulsive reaction–diffusion Cohen–Grossberg neural networks with time-varying delays. By constructing a new Lyapunov-type function and a comparison principle, sufficient conditions that guarantee the global practical exponential stability of specific states are established. The states of interest are determined by the so-called <i>h</i>-manifolds, i.e., manifolds defined by a specific function <i>h</i>, which is essential for various applied problems in imposing constraints on their dynamics. The established criteria are less restrictive for the variable domain and diffusion coefficients. The effect of some uncertain parameters on the stability behavior is also considered and a robust practical stability analysis is proposed. In addition, the obtained <i>h</i>-manifolds’ practical stability results are applied to a bidirectional associative memory (BAM) neural network model with impulsive perturbations and time-varying delays. Appropriate examples are discussed. |
| format | Article |
| id | doaj-art-e5698f715fbf4e19a227f34229341bf0 |
| institution | DOAJ |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-e5698f715fbf4e19a227f34229341bf02025-08-20T02:44:32ZengMDPI AGEntropy1099-43002025-02-0127218810.3390/e27020188On the Global Practical Exponential Stability of <i>h</i>-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying DelaysGani Stamov0Trayan Stamov1Ivanka Stamova2Cvetelina Spirova3Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USADepartment of Engineering Design, Technical University of Sofia, 1000 Sofia, BulgariaDepartment of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USADepartment of Mathematics, Technical University of Sofia, 8800 Sliven, BulgariaIn this paper, we focus on <i>h</i>-manifolds related to impulsive reaction–diffusion Cohen–Grossberg neural networks with time-varying delays. By constructing a new Lyapunov-type function and a comparison principle, sufficient conditions that guarantee the global practical exponential stability of specific states are established. The states of interest are determined by the so-called <i>h</i>-manifolds, i.e., manifolds defined by a specific function <i>h</i>, which is essential for various applied problems in imposing constraints on their dynamics. The established criteria are less restrictive for the variable domain and diffusion coefficients. The effect of some uncertain parameters on the stability behavior is also considered and a robust practical stability analysis is proposed. In addition, the obtained <i>h</i>-manifolds’ practical stability results are applied to a bidirectional associative memory (BAM) neural network model with impulsive perturbations and time-varying delays. Appropriate examples are discussed.https://www.mdpi.com/1099-4300/27/2/188Cohen–Grossberg neural networksreaction–diffusion termsimpulsespractical stabilityh-manifolds |
| spellingShingle | Gani Stamov Trayan Stamov Ivanka Stamova Cvetelina Spirova On the Global Practical Exponential Stability of <i>h</i>-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying Delays Entropy Cohen–Grossberg neural networks reaction–diffusion terms impulses practical stability h-manifolds |
| title | On the Global Practical Exponential Stability of <i>h</i>-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying Delays |
| title_full | On the Global Practical Exponential Stability of <i>h</i>-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying Delays |
| title_fullStr | On the Global Practical Exponential Stability of <i>h</i>-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying Delays |
| title_full_unstemmed | On the Global Practical Exponential Stability of <i>h</i>-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying Delays |
| title_short | On the Global Practical Exponential Stability of <i>h</i>-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying Delays |
| title_sort | on the global practical exponential stability of i h i manifolds for impulsive reaction diffusion cohen grossberg neural networks with time varying delays |
| topic | Cohen–Grossberg neural networks reaction–diffusion terms impulses practical stability h-manifolds |
| url | https://www.mdpi.com/1099-4300/27/2/188 |
| work_keys_str_mv | AT ganistamov ontheglobalpracticalexponentialstabilityofihimanifoldsforimpulsivereactiondiffusioncohengrossbergneuralnetworkswithtimevaryingdelays AT trayanstamov ontheglobalpracticalexponentialstabilityofihimanifoldsforimpulsivereactiondiffusioncohengrossbergneuralnetworkswithtimevaryingdelays AT ivankastamova ontheglobalpracticalexponentialstabilityofihimanifoldsforimpulsivereactiondiffusioncohengrossbergneuralnetworkswithtimevaryingdelays AT cvetelinaspirova ontheglobalpracticalexponentialstabilityofihimanifoldsforimpulsivereactiondiffusioncohengrossbergneuralnetworkswithtimevaryingdelays |