Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive Attacks
This article investigates the problem of finite-time synchronization of fractional-order complex-valued random multi-layer networks without decomposing them into two real-valued systems. Firstly, by promoting real-valued signum functions, sign functions on the complex-valued domain are introduced. S...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/47 |
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| author | Lulu Xu Juan Yu Cheng Hu Kailong Xiong Tingting Shi |
| author_facet | Lulu Xu Juan Yu Cheng Hu Kailong Xiong Tingting Shi |
| author_sort | Lulu Xu |
| collection | DOAJ |
| description | This article investigates the problem of finite-time synchronization of fractional-order complex-valued random multi-layer networks without decomposing them into two real-valued systems. Firstly, by promoting real-valued signum functions, sign functions on the complex-valued domain are introduced. Simultaneously, quantization functions in the complex-valued domain are also introduced, and several related formulas for sign functions and quantization functions in complex-valued domain are established. Under the framework of the given sign function and quantization function, an adaptive quantized control scheme with or without deception attacks is designed. According to the finite-time theorem, Lyapunov function, and graph theory methods, some sufficient criteria for realizing finite-time synchronization in complex-valued fractional-order multi-layer networks have been obtained. Furthermore, the setting time of finite-time synchronization is effectively evaluated. Eventually, the reliability of our results and the practicality of control strategies are verified through numerical examples. |
| format | Article |
| id | doaj-art-0808789b2af04c4d982343eaa5c83bcf |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-0808789b2af04c4d982343eaa5c83bcf2025-01-24T13:33:29ZengMDPI AGFractal and Fractional2504-31102025-01-01914710.3390/fractalfract9010047Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive AttacksLulu Xu0Juan Yu1Cheng Hu2Kailong Xiong3Tingting Shi4College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaThis article investigates the problem of finite-time synchronization of fractional-order complex-valued random multi-layer networks without decomposing them into two real-valued systems. Firstly, by promoting real-valued signum functions, sign functions on the complex-valued domain are introduced. Simultaneously, quantization functions in the complex-valued domain are also introduced, and several related formulas for sign functions and quantization functions in complex-valued domain are established. Under the framework of the given sign function and quantization function, an adaptive quantized control scheme with or without deception attacks is designed. According to the finite-time theorem, Lyapunov function, and graph theory methods, some sufficient criteria for realizing finite-time synchronization in complex-valued fractional-order multi-layer networks have been obtained. Furthermore, the setting time of finite-time synchronization is effectively evaluated. Eventually, the reliability of our results and the practicality of control strategies are verified through numerical examples.https://www.mdpi.com/2504-3110/9/1/47multi-layer networkfinite-time synchronizationadaptive quantized controldeceptive attack |
| spellingShingle | Lulu Xu Juan Yu Cheng Hu Kailong Xiong Tingting Shi Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive Attacks Fractal and Fractional multi-layer network finite-time synchronization adaptive quantized control deceptive attack |
| title | Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive Attacks |
| title_full | Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive Attacks |
| title_fullStr | Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive Attacks |
| title_full_unstemmed | Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive Attacks |
| title_short | Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive Attacks |
| title_sort | finite time synchronization of fractional order complex valued multi layer network via adaptive quantized control under deceptive attacks |
| topic | multi-layer network finite-time synchronization adaptive quantized control deceptive attack |
| url | https://www.mdpi.com/2504-3110/9/1/47 |
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