Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays
This paper studies gene regulatory networks (GRNs) with distributed delays. The essential concept of practical stability of the genes is introduced. We investigate the problems of practical stability and global practical exponential stability of the GRN model under an impulsive control. New practica...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/12/847 |
| _version_ | 1797380960069615616 |
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| author | Jinde Cao Trayan Stamov Gani Stamov Ivanka Stamova |
| author_facet | Jinde Cao Trayan Stamov Gani Stamov Ivanka Stamova |
| author_sort | Jinde Cao |
| collection | DOAJ |
| description | This paper studies gene regulatory networks (GRNs) with distributed delays. The essential concept of practical stability of the genes is introduced. We investigate the problems of practical stability and global practical exponential stability of the GRN model under an impulsive control. New practical stability criteria are proposed by designing appropriate impulsive controllers via the Lyapunov functions approach. In the design of the impulsive controller, we consider the effect of impulsive perturbations at fixed times and distributed delays on the stability of the considered GRNs. Several numerical examples are also presented to justify the proposed criteria. |
| first_indexed | 2024-03-08T20:45:26Z |
| format | Article |
| id | doaj.art-1f4e5e83b99c48d897b5c217d7350602 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T20:45:26Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-1f4e5e83b99c48d897b5c217d73506022023-12-22T14:09:57ZengMDPI AGFractal and Fractional2504-31102023-11-0171284710.3390/fractalfract7120847Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed DelaysJinde Cao0Trayan Stamov1Gani Stamov2Ivanka Stamova3Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, School of Mathematics, Southeast University, Nanjing 211189, ChinaDepartment 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, University of Texas at San Antonio, San Antonio, TX 78249, USAThis paper studies gene regulatory networks (GRNs) with distributed delays. The essential concept of practical stability of the genes is introduced. We investigate the problems of practical stability and global practical exponential stability of the GRN model under an impulsive control. New practical stability criteria are proposed by designing appropriate impulsive controllers via the Lyapunov functions approach. In the design of the impulsive controller, we consider the effect of impulsive perturbations at fixed times and distributed delays on the stability of the considered GRNs. Several numerical examples are also presented to justify the proposed criteria.https://www.mdpi.com/2504-3110/7/12/847practical stabilityimpulsesdistributed delaysLyapunov functions |
| spellingShingle | Jinde Cao Trayan Stamov Gani Stamov Ivanka Stamova Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays Fractal and Fractional practical stability impulses distributed delays Lyapunov functions |
| title | Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays |
| title_full | Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays |
| title_fullStr | Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays |
| title_full_unstemmed | Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays |
| title_short | Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays |
| title_sort | impulsive controllers design for the practical stability analysis of gene regulatory networks with distributed delays |
| topic | practical stability impulses distributed delays Lyapunov functions |
| url | https://www.mdpi.com/2504-3110/7/12/847 |
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