Stability Analysis of a Class of Neural Networks with State-Dependent State Delay
The differential equations with state-dependent delay are very important equations because they can describe some problems in the real world more accurately. Due to the complexity of state-dependent delay, it also brings challenges to the research. The value of delay varying with the state is the di...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/4820351 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556930020671488 |
|---|---|
| author | Yue Chen Jin-E Zhang |
| author_facet | Yue Chen Jin-E Zhang |
| author_sort | Yue Chen |
| collection | DOAJ |
| description | The differential equations with state-dependent delay are very important equations because they can describe some problems in the real world more accurately. Due to the complexity of state-dependent delay, it also brings challenges to the research. The value of delay varying with the state is the difference between state-dependent delay and time-dependent delay. It is impossible to know exactly in advance how far historical state information is needed, and then the problem of state-dependent delay is more complicated compared with time-dependent delay. The dominating work of this paper is to solve the stability problem of neural networks equipped with state-dependent state delay. We use the purely analytical method to deduce the sufficient conditions for local exponential stability of the zero solution. Finally, a few numerical examples are presented to prove the availability of our results. |
| format | Article |
| id | doaj-art-fb50487415804adc88d56bc95facc87e |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-fb50487415804adc88d56bc95facc87e2025-02-03T05:44:12ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/48203514820351Stability Analysis of a Class of Neural Networks with State-Dependent State DelayYue Chen0Jin-E Zhang1Hubei Normal University, Huangshi 435002, ChinaHubei Normal University, Huangshi 435002, ChinaThe differential equations with state-dependent delay are very important equations because they can describe some problems in the real world more accurately. Due to the complexity of state-dependent delay, it also brings challenges to the research. The value of delay varying with the state is the difference between state-dependent delay and time-dependent delay. It is impossible to know exactly in advance how far historical state information is needed, and then the problem of state-dependent delay is more complicated compared with time-dependent delay. The dominating work of this paper is to solve the stability problem of neural networks equipped with state-dependent state delay. We use the purely analytical method to deduce the sufficient conditions for local exponential stability of the zero solution. Finally, a few numerical examples are presented to prove the availability of our results.http://dx.doi.org/10.1155/2020/4820351 |
| spellingShingle | Yue Chen Jin-E Zhang Stability Analysis of a Class of Neural Networks with State-Dependent State Delay Discrete Dynamics in Nature and Society |
| title | Stability Analysis of a Class of Neural Networks with State-Dependent State Delay |
| title_full | Stability Analysis of a Class of Neural Networks with State-Dependent State Delay |
| title_fullStr | Stability Analysis of a Class of Neural Networks with State-Dependent State Delay |
| title_full_unstemmed | Stability Analysis of a Class of Neural Networks with State-Dependent State Delay |
| title_short | Stability Analysis of a Class of Neural Networks with State-Dependent State Delay |
| title_sort | stability analysis of a class of neural networks with state dependent state delay |
| url | http://dx.doi.org/10.1155/2020/4820351 |
| work_keys_str_mv | AT yuechen stabilityanalysisofaclassofneuralnetworkswithstatedependentstatedelay AT jinezhang stabilityanalysisofaclassofneuralnetworkswithstatedependentstatedelay |